Projectile Motion-Baseball

1. The problem statement, all variables and given/known data



At bat a baseball player hits a ball at a height of .889 m. The ball leaves the bat at 51 m/s at an angle of 81 degrees from the vertical. The ball skims the top of a 2.74 m wall as it leaves the field.

a.) Draw position, velocity and acceleration graphs describing the ball between the hit and when it leaves the field. Assume t=0 when the ball is hit, up is positive, the ball moves in positive horizontal direction, and that the pitcher's mound is the origin.

b) How long is the ball in the air?

c.) How far away from home plate is the wall?

d.) What angle relative to the x-axis is the ball moving when it passes the wall?

e.)If an infield player can jump to get his mitt 2.74 m off the ground, how close to home plate was he to still catch the ball.



2. Relevant equations



y=y₀+v₀sin(θ)t-1/2gt²

Δx=v₀cos(θ)t

For the vector components:v_y=v₀sin(θ)-gt

v_x=v₀cos(θ)

x=x₀+v_0xΔt





3. The attempt at a solution

I've drawn the graphs for part a and I am sure I have done that correctly.



I used y=y₀+v₀sin(θ)t-1/2gt² to find t which I calculated to be 10.326 s



I am confused on part C, ;the only reasonable equation seems to be Δx=v₀cos(θ)t. But if I use this equation I will need an x(final) and x(initial). I know I am looking for x(final) and I think x(initial) is -18.29. But then I will have to add this to the answer for (v₀cos(θ)t). But this does not make sense to me because I think I've already assumed 18.29 to be my origin and I've used this to calculate the time already. SO adding the 18.29 seems, to me, to be redundant.



For part e: I got an angle of 80.9 deg. And I know that should be slightly less than the launch angle. But I thought it would be a larger difference.



For part f: I am not sure what to do at all because I am not sure what the question is asking.



Thank you for your help.