# What is Maximum height: Definition and 149 Discussions

The maximum takeoff weight (MTOW) or maximum gross takeoff weight (MGTOW) or maximum takeoff mass (MTOM) of an aircraft is the maximum weight at which the pilot is allowed to attempt to take off, due to structural or other limits. The analogous term for rockets is gross lift-off mass, or GLOW. MTOW is usually specified in units of kilograms or pounds.
MTOW is the heaviest weight at which the aircraft has been shown to meet all the airworthiness requirements applicable to it. MTOW of an aircraft is fixed and does not vary with altitude, air temperature, or the length of the runway to be used for takeoff or landing.
Maximum permissible takeoff weight or "regulated takeoff weight", varies according to flap setting, altitude, air temperature, length of runway and other factors. It is different from one takeoff to the next, but can never be higher than the MTOW.

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1. ### Introductory physics: Time for a ball thrown vertically to reach maximum height

Is the answer key wrong? I keep getting the same answer and it is verified with the freefall equation distance=1/2 (g)(t^2)
2. ### [Kinematics] Calculating the maximum height reached by the ball

I realize I can solve the other way too. But I want to solve using the equations ##v = u +at## ##S = ut +0.5(at^2)## and I don't know why I didn't get the right answer. Thank you for your help!
3. ### Find Projectile Flight Time Given Only Maximum Height

I've been trying some online projectile problems. Specifically, I was using this one on master difficulty, looking at row e. It uses a random number generator; I shared the data I received in the Homework Statement above. According to the help section, you can solve this with the formula...
4. ### Calculating Maximum Height: Confusion & Solutions

I am calculating it like this: 𝑦=ℎ0−0.5𝑔𝑡^2=0→ℎ0=0.5𝑔𝑡^2→𝑡=sqrt(2*ℎ0/g) 𝑥=𝑣0*𝑡→ substituting t →𝑥=𝑣0*sqrt(2*ℎ0/g) 𝑑𝑥/𝑑ℎ0=𝑣0/(𝑔*sqrt(2*h0/g))=0 for maximum ℎ0=0. confused. can someone tell me how I am calculating this wrong?
5. ### Projectile motion with (constant) wind velocity

Let me start be making a small sketch of the problem, shown to the right. If the range of the projectile on a still day ##R = v_{0x}T##, then on the windy day the range becomes ##R+2H = v'_{0x}T = (v_{0x}+v_w) T##. Since the maximum height attained by the projectile ##H =...
6. ### MHB Computing projectile's maximum height and range.

Hi, Here is the question. Answer given is d. But i don't understand how is that computed? I am working on this question. Meanwhile any member knowing the correct answer may help me in finding out correct answer.
7. ### Maximum height a block reaches after separating from a curved moving ramp

Diagram attached at the endI personally think there's something wrong with this question, and I'd like if someone can tell me whether it's the question that is wrong or my approach. If I attempt the solution thinking that M should be stationary, the solution is simple. 0 - 1/2 mv^2 = -mgh...
8. ### Finding the maximum height of a projectile

Using the equations for constant acceleration, we can write the following set of equations for this problem: We have the following known physical constraints: Solving the above system of equations and constraints with a computer algebra system: So, all the solutions I found make...
9. ### Maximum height for water from a fire hose

Homework Statement Fire hose has diameter of 4.0 cm and flow rate of 10 L/s. There is pressure of 2.2 bar inside the hose. How high the water can go at best? Water density is 1.00E3 kg/m^3 and air pressure outside the hose is 1.0 bar. Homework Equations Flow rate $$Q = Av$$ Newtons...
10. ### Swinging Tarzan: Solving for Maximum Height & Angle

Homework Statement Tarzan runs at 6 m/s and grabs a vertical vine (negligible mass) of length 4.1 m which is tied to a branch at the top. Tarzan then swings up. Determine the maximum height Tarzan will swing up and the maximum angle the vine will make with respect to vertical. Homework...
11. ### Kinematics: find maximum height

Homework Statement A rocket takes off from the launch pad and moves directly upward with an acceleration of 29.4 m/s2. It runs out of fuel after 4s and continues to coast upward, reaching a maximum height before falling back down to Earth. a) Find the rocket's maximum height. b) What is the...
12. ### Projectile Motion Kinematics: Finding maximum height

Homework Statement A ball is kicked with an initial speed of 20m/s at an angle of 50° above the horizontal. What maximum height does the ball reach? Homework Equations Vfx=VicosΘ Δx=VicosΘt Vfy=(VisinΘ)+ay⋅t (Vfy)^2=(VisinΘ)^2+2ay⋅Δy Δy=1/2(Vfy+(VisinΘ))⋅t The Attempt at a Solution I...
13. ### What Is the Maximum Angle Attained by a Particle Projected from Earth?

Homework Statement A particle is projeccted from the surface of the Earth with an initial speed of 4km/s.Find the maximum angle attained by the particle.Radius of the earth=6400km and g=9.8m/s2 Homework Equations KE1+U1=KE2+U2 [/B]The Attempt at a Solution So I tried to proceed by this...
14. ### Maximum height of a spring toy launched at an angle

Homework Statement A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy? Homework Equations Δt = 2(V1)Sinθ/(acceleration) ΔD = V1Δt + 1/2(acceleration)(Δt^2) The Attempt at a Solution First I solved for...
15. C

### Maximum height from which a cuboid can fall and not be damaged

1. Cuboid of height h is made out of material with density ρ=1000kg/m3 and it can endure highest pressure of σ=90kPa.Cuboid is falling from the height H. When the cuboid hits the ground its centre of mass is at the height h/2.Then starts deformation of the body. During the deformation centre of...
16. ### Maximum height reached by object released from a vertical spring

Mentor Note: thread moved, therefore no template A mass m is placed on a vertical spring and allowed to reach equilibrium, whose level is ##e_0## below the original level of the spring before placing the mass. It is then pushed downwards such that it is now a distance ##x_0## below the...
17. J

### Maximum height a waitress can push on a glass without it tipping

Homework Statement I have attached the problem. I will write it out: A waitress attempts to push a glass of water of heigh 15.o cm and diameter of 7.00 cm on a dining table, as shown in the figure. If the coefficient of static friction between the glass and the table's surface is 0.350, what...
18. C

### Projectile motion -- how long does it take the projectile to reach maximum height?

Homework Statement A projectile was launched at 70 m/s at an angle of 45 degrees above the horizontal, how long does it take the projectile to reach maximum height? Homework Equations Vyo= initial vertical velocity Vo=initial velocity The Attempt at a Solution I tried using the...
19. ### How does drag force change the maximum height of projectile?

How does air resistance change the maximum height of a projectile ?
20. ### What is the Maximum Height of this projectile?

Homework Statement A projectile is launched at 750 meters per second at a 30 degree angle to the horizon. How long is it in the air? How far does it go? What is the maximum height that it reaches? Homework Equations Sin(30)=1/2 Cos(30)=sqrt(3)/2 The Attempt at a Solution This is what I have...
21. ### Finding maximum height of a string before it goes slack

Homework Statement A mass m is suspended by a light elastic string. When the mass remains at rest it is at a point 0, which is a distance a + b below the point from which the string is suspended from the ceiling, where a is the natural length of the string. The mass is pulled down a distance h...
22. J

### Dynamics how to calculate maximum height on incline

Homework Statement A 5.0kg block initally traveling at 11m/s moves up a 30degrees incline. A frictional force of 9.4N acts on the block as it moves up the incline. What maximum vertical height, h, will the block reach? m = 5.0kg, vi = 11m/s, vf = 0m/s, Fr = 9.4N, Homework Equations...
23. ### Maximum height after a collision (general solution)

Here's the situation: A small block of wood of inertia mb is released from rest a distance h above the ground, directly above your head. You decide to shoot it with your pellet gun, which fires a pellet of inertia mp. After the block has fallen a distance d, the pellet hits it and becomes...
24. ### Conservation of energy/Finding maximum height

Homework Statement A 28-kg rock approaches the foot of a hill with a speed of 15 m/s. This hill slopes upward at a constant angle of 40.0∘ above the horizontal. The coefficients of static and kinetic friction between the hill and the rock are 0.75 and 0.20, respectively. a)Use energy...
25. ### A ball being hit, find the energies and maximum height

Homework Statement The longest homerun hit by Miguel Cabrera in the 2012 season occurred at Comerica Park and had an initial y-component of velocity of 19.8 m/s and an initial x-component of velocity given as m/s, where is some value left undetermined. Assume the ball left the bat 1.22 m off...
26. ### What is the Maximum Height Achieved by a Soccer Ball Kicked at a 45° Angle?

Homework Statement A soccer ball is kicked at a 45° angle. If the ball is in the air for 3 s, what is the maximum height achieved Homework Equations y=viy + 0.5 x ay x t The Attempt at a Solution i used trig to get the vertical and horizontal components i got 2.2 for each side (as there the...
27. ### The speed of a projectile when it reaches its maximum height

Homework Statement The speed of a projectile when it reaches its maximum height is one-half its speed when it is at half its maxi- mum height. What is the initial projection angle of the projectile? Homework Equations Vf2 = vi2 + 2axThe Attempt at a Solution I know that the speed at the top...
28. ### Maximum height of a spring toy

Homework Statement A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy? Homework Equations Δ[/B]dv = v1Δt + 1/2aΔt2The Attempt at a Solution [/B] Calculate time: Δt = 2.3 m/s / 9.8m/s2 = 0.23 s Now...
29. ### Maximum height over which water can be siphoned

Homework Statement A student siphons water over a 8.5 m high wall at sea level. She then climbs to the summit of a mountain (elevation 4390 m , atmospheric pressure =58.5 kPa) and attempts the same experiment. Comment on her prospects for success. Homework Equations Bernoulli's equation...
30. ### Maximum height water can be projected onto a wall

Homework Statement H3-1 Determine the maximum height on the wall to which the firefighter can project water from the hose if the speed of the water at the nozzle is 20 m/s. The firefighter stands 18 m away from the wall and holds the nozzle 1.2 m above the ground. Homework Equations The...
31. ### Finding the rock's theoretical maximum height.

Hello everyone. So I have this one question which I thought was going to be pretty easy, but now I struggle with it. It says: 1. The question A rock is thrown vertically up in the air with an initial velocity of 0.75ms-1. What would the rock's maximum theoretical height be? I am currently in...
32. ### Maximum height of CM of a rotating stick

Homework Statement [/B] A uniform stick is held horizontally and then released. At the same instant, one end is struck with a quick upwards blow. If the stick ends up horizontal when it returns to its original height, what are the possible values for the maximum height to which the center...
33. ### Projectile Motion: Finding the Maximum Height of a Football

A football is kicked from a tee to start the football game. If the ball is kicked at a 38 degree angle with an initial velocity of 27.1 m/s, Find the maximum height of the football as it flies through the air. I was using these equations: Voy = Vo(sine of theta) Vy = Voy + at y = 1/2(a)(t^2)...
34. ### Work-kinetic energy theorem - model rocket velocity/height

Homework Statement A student experimenting with model rockets measures the speed of a vertically-launched rocket to be 18.0 m/s when it is 75.0 m above the ground on the way up. The rocket engine fires from when the rocket is at ground level to when it is 8.75 m above the ground. If the rocket...
35. ### Confused...calculating energy in a spring before launch of a ball

Homework Statement So a little background before stating the problem: During a lecture a couple weeks prior to lab, the instructor did an example where we were told to find the max height of a ball launched upwards by compressing a spring. In order to calculate that, he showed that E1 is the...
36. ### Maximum height of ball with changing acceleration

I put basic on this because my maths skills are exactly that and I suspect the answer to this question will be fairly maths heavy. I understand that the equation to calculate the maximum height of a projectile (ignoring wind resistance) is Hmax = (Vf2 - Vi2)/2a But this only works over small...
37. ### Finding the time and maximum height at highest point

Homework Statement :[/B] A projectile is given initial velocity 80 m/s ( V0 ) at angle 60° above the horizontal. Find the time it takes to reach to the highest point and find the maximum height. (g = -10 m/s2) Homework Equations :[/B] 1. y_{final} = y_{initial} + v_{y_{initial}}t + \frac...
38. ### Communicating vases, maximum height before rest (water in pipes)

I do not know much about computers too (not really true but I am not really up to date), I do not know if I am doing what I am supposed to, here is my first simple question: Two connected pipes, equal diameter (internal) 100 mm, same height (2200 mm), I have water in one pipe at 2000 mm, in the...
39. ### MHB Very dificult: The minimum perimeter and maximum height of a triangle under constraints

Obtain -The maximum height corresponding to the side b of any triangle (abc) once known the value of its perimeter and height corresponding to the a side a. -The minimum perimeter of any triangle (abc) once known the heights corresponding to the a and b sides. Aux: Geogebra construction...
40. ### Maximum Height of a Thrown Stone with Air Resistance

Homework Statement A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Air resistance is proportional to speed, with k=1/128 lb-s/ft. Find the maximum height attained by the stone. Homework Equations None. The Attempt at a Solution Here's...
41. ### Maximum height at which a siphon can drain an open water tower

Homework Statement If you have a water tower (basically a cup) open to the atmosphere, with a siphon (basically a straw) inside it as shown below: (sorry assume the height h extends to the bottom of the cup instead of only part way - would that change anything though?) Then what is the...
42. ### What is the maximum height of the square's center-of-mass?

Homework Statement A square shaped block of mass m travels to the right with velocity v on a frctionless surface. The block has side-length 2d. The block hits a very small, immovable obstacle on the floor and starts to tip. The block has moment of inertia Icm=2/3md^2 about an axis through...
43. ### How High Does the Apple Reach When Thrown at 55 Degrees?

Homework Statement You want to throw an apple to your buddy on the second floor balcony that is 2.2m above where you release the apple. When you throw the apple with a speed of 14m/s at an angle of 55° above the horizontal, it gets to your buddy who catches it on the way down. Find the maximum...
44. ### Time to reach maximum height

Homework Statement find time to reach max height max height is 0.870m mass of diver is 70kg makes an angle when diving of 85 degrees Homework Equations Vf=Vi + gt The Attempt at a Solution Vi=0 Vf=gt t=vf/g = 0.870/9.8 not sure if this the right approach
45. ### Maximum Height of model rocket

Homework Statement A model rocket is launched with an initial velocity of 55 m/s. Its height as a function of time can be modeled by h(t) = -4.9t2 + 55t. Determine the maximum height reached by the rocket.Homework Equations h(t) = -4.9t2 + 55tThe Attempt at a Solution h'(0) = 55, since h'(t) =...
46. ### Impulse and maximum height of a particle

Homework Statement A particle receives an impulse that lasts 1s, coming from a upwards vertical force. This force is given by the following equation: F = -8t²+8t. What is the maximum height reached by the particle?Homework Equations F = -8t²+8t The Attempt at a Solution \int(-8t²+8t)dt =...
47. ### Kinematics - projectile motion - time to maximum height?

Kinematics -- projectile motion -- time to maximum height? Homework Statement The nozzle of a fire hose discharges water at a speed of 10 m/s. The nozzle is aimed straight up. How long does it take for a water drop to reach its maximum height? Start with translating the question: vi= 10 m/s...
48. ### Maximum height of a projectile thrown from a rooftop

Homework Statement A man stands on the roof of a building of height 14.6m and throws a rock with a velocity of magnitude 30.8m/s at an angle of 33.2∘ above the horizontal. You can ignore air resistance. Calculate the maximum height above the roof reached by the rock. Homework Equations...
49. ### Angle at Maximum Height

Homework Statement the initial velocity of a projectile is 150 m\s .the angle between the velocity vector and the trajectory at the projectile's maximum height is a) 90 b) 45 c) zero d) 63.1 e) 36.9 Homework Equations Vox= vx = Vocosθ Vy = Vosinθ-gt Range (R) = (vo)^2*sin(2θ)/g...
50. ### Speed at Maximum Height and Initial Velocity

Homework Statement An ball is launched at a 45 degree angle with an initial speed v0. What is its speed at its max height? Homework Equations n/a The Attempt at a Solution This problem does not contain any calculations. I was wondering if somebody could explain how the speed at...