Projectile motion Definition and 1000 Threads

Imagine we kick the ball from point ##\text{A}## with horizontal speed ##u_x^{\text{initial, A}} = v \cos \alpha## and vertical speed ##u_y^{\text{initial, A}} = v \sin \alpha##. The gravitational acceleration is ##\vec g##, the x-axis points towards the wall, the y-axis points upwards. The...

Wild question. Even Chat GPT struggling. What I first attempted was to find the velocity by which the projectile with v1 falls down to the ground with. This part was easy. Kinetic energy gained = gravitational potential energy lost Let's define our coordinate frame as up vectors being positive...

I'm not sure where the equation E_k=(gmR^2)/4h comes from & I also don't really know where to start either :(

I don't know if i'm exactly right. But I started with x(time) = V cos θ t which = (6810 m/s) cos (69.1°) (11.4 * 10^-3 s) is ... 27.69 m & since Electric field due to uniformly charge surface is represented by... E = (q * σ)/(2 * ε_0 * m), and since acceleration (a) can be expressed as F/m...

initial velocity y component is (cos30) * 20. t = 25m / ((cos30) * 20)m/s = 1.45 seconds d = vt + .5at^2 v= 20sin30 v= 10 , d= 10(1.45s) + .5(-9.8m/s^s)(1.45s)^2 d=4.2m 4.2-2.5 = +1.7m, so the ball will not hit the fence I need confirmation please

Is it possible to trace the trajectory of an object using only its velocity and position, both of which are given as components. My method of doing so involves using the time until max height is reached, and using that time value to calculate the max height itself (h,k), then plugging in the...

I am attempting problem number 2.38 from John R. Taylor's Classical Mechanics and I am not getting the correct answer. My procedure is as follows: Equation of motion (taking up as the positive direction): $$m\dot{v}=-mg-cv^2$$ Now to find ##v_\mathrm{ter}##, the terminal velocity, we consider...

Hey so I encountered a problem recently, which while being simple, gave me another problem that I couldn't solve. The problem: An object is launched vertically upward with an initial velocity of 10 m/s from an elevation of 20m and allowed to hit the ground. Develop the equations of motion...

TL;DR Summary: Using vector functions how can I find the minimum average velocity (something greater than 11.86m/s) of a ball if the launch angle is unknown and if I have a point that the object must travel through (11.86, 3.47)? In my assignment, I developed a function for a lob shot...

If f(x) is the function of the "ground": My first assumption is that in a certain $$\bar{x}$$, $$f''(\bar{x})=0$$, and from that point I will analyse the situation. The object has initial energy $$E_0=\frac{mv^2}{2}+mgf(x),$$ then $$v=\sqrt{\frac{2}{m}}\sqrt{E_0-mgf(x)}.$$ In each point the...

TL;DR Summary: I want to mainly figure out where in the problem solving I went wrong. I understand the correct answer (since I looked it up), but to me, it does not make any sense. I am honestly stumped at this point. Online solutions say that my equation y = 0.5774x-0.003354x^2 should...

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 -...

Top-Down-Perspective: At first I am quite sure that the problem is not solvable since there are that many unknowns. But my Approach would be to create a linear function with P1 and P2 and then set it equal to the function that gets me the impact location of P3 and then solve it by b3. Thanks...

My reasoning was to use this kinematic equation to first get time of flight of the baseball using horizontal components, and then use this same equation again to find initial velocity.

I worked myself into a trigonometry rut. I've tried two approaches, first by not changing the frame of reference, and second by taking the incline as the horizontal x axis. Here is my second attempt: Take the incline as the horizontal. Then the coordinates of target T are: $$ \begin{align} x_T...

We know x = R =max range (28m) on level ground. Need to find v()^2. Subbing y=0 into (1) above, get v(0)^2 = (gR^2/)/(2*cos (theta)^2 * tan (theta). ... (2) This didn't seem right, since this means v(0)^2 is a negative number ... maybe my orientation or algebra wrong? Anyway, didn't see...

26.6m/s = v0 36.5º = θ g = 9.81m/s^2 A) Find Range: (v0^2)/g *sin2θ = (26.6^2)/9.81 * sin2(36.5) = 89.99 I double-checked with the other Range equation (2v0*cosθ * (v0sinθ)/g) so I know I'm doing something wrong. Please help! Thank you edit: A) Correct answer is 69.0

Vertical position (x component): y(t) = y0 +v0 * t -1/2*g*t^2 Position yx(t) = 0cm = 40cm + 0 *t -1/2 * 981cm/s/s * t^2 edit: I replaced v0 = 0 and got t = 0.286s, which is incorrect according to the submission. This didn't work so I thought maybe by finding the angle of the throw would help...

I assumed the cyclist was going 60-kph. Then worked backwards as shown above to calculate the deceleration in the x direction and then the time to decelerate to a stop at 39 m. Then used this time to calculate the initial speed if cyclist thrown 39 m, which was 8.4 m/s. But if he was going...

Hi, so I solved this using energy. I also tried solving this using kinematic equations. The issue I am running into s for calculating the Vy of the problem. I am able to find the time it takes the rock to fall using d=(1/2)gt^2. Then, I considered two different ways of going about finding the...

So first I found the velocity of the ball at the bottom of the swing from the force equations, which I got to be 4.9 m/s and this is only in the x-direction. Then using the projectile motion for delta y I found time, which is 0.2s. Then using that time I found the delta x to be 0.98m. I just...

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?

If we throw a ball with initial velocity v0, and the ball progresses in a projectile motion, ignoring air resistance, will there be a force in the x direction? If so, what is that force in the x direction's value mathematically? I know there is a force in the y direction due to gravity.

Givens: Vyi=12.5 m/s Vyf=-12.5 m/s (at the same horizontal level) ay=-9.81 m/s^2 Δy= zero m (as the displacement on the y-axis, when the projectile reaches the same horizontal level, is zero m) Δt=? When I use Δy=[(vyi+vyf)/2]*Δt I get the time as undefined. Δt= 2Δy/(vyi+vyf) = 2*0 m/(12.5...

Hello everyone, I have a homework about projectile motion experiment and I threw small ball over the table and ball did projectile motion at the end of the table and ı recording this motion on motion tracker and motion tracker gave me acceleration of y component of ball as 14.02 m/s^2. But it...

I would like to conduct an experiment asking the question "how does the angle at which a projectile is launched vary with respect to the horizontal range it covers?" Ultimately, I'd like to prove that the horizontal range is directly proportional to sin(2(theta)). This will be done with the aid...

(a) ##u_{min}=\big(1+\frac{m_2}{m_1}\big)\sqrt{2\mu_k g d}## (b) ##x_f=\sqrt{\frac{2h}{g}\Big(\big(\frac{m_1}{m_1+m_2}u\big)^2-2\mu_k g d\Big)}## Can someone check please?

When a ball is thrown such that it moves in a curved trajectory in the horizontal plane, it amuses me to think of its dynamics. In motion of a ball thrown upwards the force of gravity gives it a parabolic trajectory However when the ball is thrown to curve and hit a target, (in the horizontal...

So far all I have determined is the equations of motion for the two and that is as follows. It is trivial that y(t)=v1sin(Q)t -gt^2/2 and that x(t)=v2cos(Q)t. Now the angle that is anticlockwise from the negative horizontal of the robber is 90 - Q using basic trigonometry, using this we can...

##V_x = V_0 cos \theta ## ##x = V_0 cos \theta t## ##V_y = V_0 cos \theta ## ##y = V_0 cos \theta t## ##F_x = m\ddot{x}## ##-mgsin \phi = m\ddot{x}## ##\dot{x} = -gtsin\phi + V_x## ##x = -\frac{1}{2} gt^2 sin \phi + V_x t## ##x = -\frac{1}{2} gt^2 sin \phi + v_0 cos\theta t## ##F_y =...

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i have no clue how to start please help me

Looking for some guidance on how to set up the equations for a projectile intercept given that you have perfect information about the target velocity, size and weather conditions in a 3D scenario, it's for an amateur videogame that I'm developing in my spare time For simplicity sake let's...

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 =...

I'm having a bit of a problem with some projectile motion. The standard motion is not a problem, but how to I compensate for a projectile that is rotating or tumbling backwards (nose over tail) at a significant rate of speed. The Tumble rotation is about 50 degrees/second on a cylindrical...

1)Find the range of the gun when the muzzle speed is 400m/s and the elevation 24.5° - I tried to find " Time " via t= [v-u]/a by substituting it through cos--> t= ( 0- [400cos24.5] )/-10 and got [ 36.39 ]. Which I then substituted in S=ut---> S= ( 400cos24.5 ) x 36.39=13245.3. [ the answer...

I sketch a diagram for the problem and show it to the right. My approach is going to be along the following lines : (1) Use the equation of motion in the ##x## direction to express the total time of flight ##T## as a function of the range and initial angle ##T = T(R, \theta_0)##. (2) Plug this...

Let: ##x## = horizontal distance from person to tree ##h_t## = height where arrow hits the coconut (measured from ground) ##h_o## = height of monkey ##u## = initial speed of arrow ##\theta = 35^0## ##t = 1~ \text{s}## Vertical displacement of coconut until it is hit: $$h_t - h_o = -\frac{1}{2}...

Hi everyone. I'm a new member, great to be here:) I have a few questions that I wanted to ask you guys regarding the method by which we implement the Runge-Kutta approximation of Projectile Motion if we should do it using a numerical iterative method with a Spreadsheet like Excel. I have...

I know the conventional method for solving this question using the formula for maximum range of a projectile in an inclined plane, but since it is an objective problem, if we consider a non general case where α=0, then clearly we can see that (see attachment) only one option matches which...

So i have this question. If a projectile is fired from a spring loaded system and when it goes pass a chronograph, reads 300FPS and has a mass of 0.12grams. Is there any way to use the proportionality theorem (1/3=x/6 example) to approximate how fast a mass of 0.25grams is when fired from same...

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Hey Everyone, my physics teacher has assigned us a task which involves predicting the range of a ball falling down an inclined plane into a free-fall, the equation for the final velocity of the ball down the ramp, accounting for rotational velocity has been provided, this is the initial velocity...

Total acceleration equaled = -9.81

I don't need to know how to solve this but I was just looking for the answer. Can anyone help? A man is standing at a launch site. The rocket doesn't liftoff. Frustrated s/he throws it straight up with a speed of 12.42 m/s. It is caught on the way down at a point 5.0 meters above where it was...

I know I need to solve for acceleration as I am not on Earth and I am assuming I should create a distance vs. time graph. But overall I am unsure what to do. Please help been stuck on this for a while.

Summary:: Scooby-Doo wants a Scooby Snack. According to a website I looked up last night, Scooby can run at a speed of 36 km/h. He runs up a ramp (as shown, 2.0 meters high, 4.0 meters long) at that speed and off the edge. Three meters from the end of the ramp, Shaggy has a Scooby-Snack...