Launch angle Definition and 53 Threads

For this problem, The solution is, I don't understand how they got from ##\frac {sin^2\theta_i}{sin2\theta} ## to ##\frac{tan\theta_i}{2}##. Would somebody please show me the immediate steps? I also don't understand is why they say the ignore the trivial case where ##\theta_i = 0~rad##...

i used t=d/v for the x direction using the formula t=250/vcos55 and subbed that into the formula for the y direction d = (v) (t) + (0.5) (a) (t)^2 35 = (vsin55) (250/vcos55) - (4.9) (250/vcos55)^2 canceled out the first two v 35 = sin55 (250/cos55) - (306250/v^2cos3025) 35 = 357 -...

if the target is lower than me, the formula is below, but if it's higher as in the task, a whole different formula is required I think. a = 9.8 * distance^2 / velocity^2 phi = Arctan(distance / height_diff) angle_if_elevation = ( Arccos((a - height_diff) / Sqroot(height_diff^2) + distance^2)) +...

I am trying to find the launch angle ##\theta## using the relationship: ##\theta=\arctan(\frac{v_{y}}{v_{x}})## So, ignoring attenuation due to air resistance, we have a constant horizontal velocity: ##v_x = d_x/t = 95m/4.5s \approx 21 m/s## But what value do we use for ##v_y## which is not...

In a process of writing a game. Effectively need to know how to angle the barrel for the projectile to hit the selected target. So for the equation y = h + x * tan(α) - g * x² / 2 * V₀² * cos²(α) Everything except α is known. Could anyone more wise in the ways of science than me help me solve...

I don't know the distance or the horizontal velocity so I can't find any logical solution

the mass is 0.8kg speed is 50m/s distance is 100m

Hi, I am new here to the forum and I am having trouble with a project that I am undertaking with some friends. We are trying to build a firefighting robot. I am trying to derive an expression to solve for the launch angle theta of the water so that at x (meters), the projectile will be at 0.33...

Homework Statement Hello, so I’ve been trying to find some possible way to calculate this: The initial Velocity and angle needed to launch a projectile and reach the coordinates (x,y). The maximum height the ball can reach before it starts to head down to the target value should be y+5m The...

Homework Statement A hunter aims a high velocity semi-automatic rifle at a moose that is 500.0 m away in a direct line of sight. The moose stands 40.0 m below the horizontal in a depression with a bog at the bottom. The muzzle velocity is 2500.0 feet per second and the sight on the rifle is...

Homework Statement How to prove the correlation between launch angle (<45°) and horizontal displacement. Independent Variable: Horizontal distance Dependent Variable: Launch Angle (Important) Controlled Variable: Firing velocity [90 m/s] Another problem is, with the data that I have...

Homework Statement I'm about to conduct an experiment about factors that affect the flight of an elastic band. The aim of this experiment is to find how the angle of launch, when shooting a rubber band, affects the range or distance of the shot. Do you suggest to consider the drag force? like...

Homework Statement I'm doing a lab report about how the launch angle affects the range of a projectile. Independent Variable Angle of Launch Dependent Variable Range or distance I did an experiment with three trials and here are my results: And then plotted the data. However, it's a...

Homework Statement Find the angle at which the projectile is launched. (Hint: use tan^2+1=sec^2) Initial Net Velocity=430 m/s The projectile lands perfectly on the edge of a cliff 80 meters high and 175 meters away. Homework Equations tan^2+1=sec^2 Kinematics, i.e.- v=vo+gt...

Homework Statement A ski jumper leaves the ski track moving in the horizontal direction with a speed of 25.0 m/s as shown in Figure 4.14. The landing incline below her falls off with a slope of 35.0°. Where does she land on the incline? I've attached an image of the problem, my work is below...

Homework Statement The mountain rescue officers trigger the avalanche by firing a gun at a distant mountain slope. The muzzle velcoity of the gun is 225m/s. The horizontal and vertical distance from the gun to the slope is x=1,072m and y=538m respectively. Find the lowest angle between the...

Homework Statement You are an invading army who wants to launch a rock over the enemy castle’s wall. The wall is 12 meters high and there is a moat surrounding the wall which forces you to launch from a distance of 17 meters away. What angle and velocity should you shoot at in order to just...

Hello. In one of my engineering classes we are doing a computer programming project that requires us to use Newton's second law to find an equation that that would give us the max distance traveled by an object launched off a cliff at a known height of H and an initial velocity of Vo. Then with...

I need some help working the following problem. I have everything answered except #5 and that is where I get lost. Any help would be greatly appreciated. Suppose a field goal kicker (American football) can kick the ball at a launch speed of 58 miles/hour. If the ball is placed at the...

Hi guys, I was working on a formula for the optimal angle for simple point-like projectiles free-falling under a uniform g-field but I got stuck. after a simple derivation , I obtained the following equation: R=(vcos(@)/g)(vsin(@)+((vsin(@))^2+2gh)^0.5) where R , @ , h are respectively the...

Homework Statement A cannon is supported one meter above the top of a 20 degree declining slope of length 200m. The cannon has a launch velocity of 55m/s. There is a ball halfway down this slope moving at a constant velocity of 20m/s. -Determine the angle \Theta required for the projectile to...

Homework Statement The range of a projectile is 483m, and it reached a maximum height of 65m. What were the initial speed and launch angle of the projectile? Assume the start and finish heights are equal. Homework Equations The Attempt at a Solution I just need a push in the...

Homework Statement A bean bag launcher is used to shoot a bean bag at a corn hole board. The bag is released at a height of .61m above the ground. The front of the board is 5.18m from the location where the launcher releases the bean bag. The back of the board stands .31 m off the ground; the...

The Question: A water balloon is fired 34 m/s from a water cannon, which is aimed at an angle of 18° above the ground. The centre of the cannon's target (which has a radius of 1.0m) is painted on the asphalt 42m away from the water cannon. a) Will the balloon hit the target? Justify your...

Hey everyone, I've been trying to do a problem in which I attempt to find the angle that maximizes the horizontal distance of a rocket, which has a stage with thrust and then a stage as a projectile. After a delay period, an ejection charge fires and causes the rocket to drop straight...

Homework Statement A cannon fires at a hilltop target with a muzzle velocity of V = 600 ft/s. The horizontal and vertical distances to the target are L = 0.5 miles and h = 0.25 miles. Determine the elevation angle at which the cannon should be fired. L=2640 ft h=1320 ft...

Greetings to all. First off, I apologize if I come off as an idiot here who has no idea what he's talking about (probably because I don't). My career is basically as a graphics designer, programmer, and musician- in that order (I design and build iOS applications for a living). I understand...

Edit: I solved my problem for launch angle. So now I have another question. I am writing a script for a cannon in a video game that will aim at XYZ coordinates by determining the angle and bearing needed to launch the projectile to hit the target. I wish to add a target-leading formula so...

Homework Statement Vy - 15m Vx - 40m U - 17m/s V - 0 Time to reach highest point (t) 1.7s Homework Equations cos 0 = a/c The Attempt at a Solution 72 degrees. Not sure if this is the correct method of calculating the angle, especially since a projectile's trajectory is a...

Homework Statement A hot-air balloon rises from the ground with a velocity of (3.00m/s)y. A champagne bottle is opened to celebrate takeoff, expelling the cork horizontally with a velocity of (4.00m/s)x relative to the balloon. When opened, the bottle is 5.00m above the ground. What is...

I wasn't able to figure this problem out, so I looked at the answer. The answer is 19.06 degrees and 2.116 seconds. Using these values in the kinematic equations, I calculated that at x=200 ft, the height of the projectile is y=50ft. When x=200ft, shouldn't y=0ft? I thought the problem is asking...

1. OK so if you imagine a projectile is fired with an inital velocity (u) of 400 m/s at an angle theta. What two values of theta will cause the projectile to hit a point b that is 5 km horizontally away from the point of launch and 1.5 km vertically? u (magnitude)= 400 m/s deltaH = 1500 m (1.5...

Homework Statement An artillery gun is trying to hit a target that is 12.5 km away. If the shell is fired at 650 ms-1 at what angle above the horizontal should the gun be fired to hit the target assuming that air resistance is negligible? [g=9.8 ms-2] Homework Equations I tried using v^2_y...

Calculus based course, this is from the "linear momentum of a system of particles" section. I've attached a rough sketch of the graph from my textbook. The main points of the graph are this, it's a parabola, at T=0 and T = 4.5, P(momentum) = 6. At T= 2.25 (maybe) it bottoms out. I say maybe...

[SIZE="2"]Moderator's note: two threads merged into one. -- Redbelly98 Homework Statement what is the relationship between the launch angle and the displacement of a projectile, is it possible to say that the launch angle is proportional to displacement, can it be done mthematically by...

Homework Statement Find the arc length of the projectile from launch until the time it hits the ground, given that 0 V is 100 feet/sec and is 45 degrees. Homework Equations Arc Length= ∫_a^b▒√(█(1+(f^' (x) )^2@)) dx Arc Length of Curve= ∫_a^b▒〖v(t)dt=∫_a^b▒√((dx/dt)^2+(dy/dt) )〗^2...

Homework Statement Basketball player throws the ball form the middle of the court one second before the game ends. How much must the initial velocity of the ball be and at what angle it must be thrown, if it should hit the basket at the exact time of siren without preceding reflection from...

Homework Statement On a hot summer day, a young girl swings on a rope above the local swimming hole . When she let's go of the rope her initial velocity is 2.10 m/s at an angle of 35.0 degrees above the horizontal. If she is in flight for 0.615 s, how high above the water was she when she let...

Homework Statement at 1/2 of its maximum height, the speed of a projectile is 3/4 of its initial speed. what was its launch angle?(ignore any effects due to air resistance.) Homework Equations The Attempt at a Solution I don't even know where to begin.

Homework Statement Suppose a very narrow, very tall wall of height H stands between two children who are trying to play catch. The wall is a distance x[SUB][wall] from the thrower, and the catcher is distance X[SUB][F] from the thrower. In this problem you will calculate the lunch angle...

URGENT! General Launch Angle Problem Homework Statement A batted baseball leaves the bat at an angle of 25.0 above the horizontal and is caught by an outfielder 370 ft from home plate at the same height from which it left the bat What was the initial speed of the ball? How high does the...

Homework Statement A basketball is thrown horizontally with an initial speed of 4.20 m/s. A straight line drawn from the release point to the landing point makes an angle of 30.0° with the horizontal. What was the release height? Vox=4.20 m/s=Vx Ax=0 Voy=0 m/s Ay=-9.81 m/s^2 Theta=180*-30.0*...

General Launch Angle (Vectors) PLZ HELP URGENT Homework Statement In a friendly game of handball, you hit the ball essentially at ground level and send it toward the wall witha speed of 13m/s at an angle of 24 degrees above the horizontal. a) how long does it take for the ball to reach the...

Homework Statement A catapult on a cliff launches a large round rock towards a ship on the ocean below. The rock leaves the catapult from a height H of 32.0 m above sea level, directed at an angle q above the horizontal with an unknown speed v0...

Homework Statement An object was launched from the top of a cliff at some angle with an acceleration of 50 ft/sec that overcame gravity. The fuel tank ran out after 2 seconds of flight and gravity took over from that point forward. The object reached a maximum height of 310 ft, was in the air...

Homework Statement Fairgoers ride a Ferris wheel with a radius of 6.00 m, the bottom of which is 1.75 m from the ground. The wheel completes one revolution every 28.0 s. A passenger drops his keys when he is three quarters of the way up and at an angle of 45° to the vertical. Where do the keys...

Homework Statement At .5 of its maximum height, the speed of a projectile is .75 of its initial speed. What was its launch angle? Homework Equations (1)V1y = V0y - gt (2)y1-y0 = V0yt - .5gt^2 The Attempt at a Solution The part that really bothers me is the second part of the first statement...

A golfer gives a ball a maximum initial speed of 28.5 m/s. (Neglect air resistance.) (a) What is the longest possible hole in one for this golfer? Neglect any distance the ball might roll on the green, and assume that the tee and the green are at the same level. m (b) What is the minimum speed...

I have a problem that I'm having trouble with. The question is, A farris wheel that has a radius of 5 meters, takes 32 seconds to complete one revolution. (a) what is the average speed of the rider on the Ferris Wheel? (b) If passenger drops keys when at top of the wheel, where does it land...

The launching speed of a certain projectile is 5.2 times the speed it has at maximum height. What is the elevation angle at launching? Could someone just give me a starting point or a hint in the right direction? I know that the horizontal velocity doesn't decrease, and the vertical...