Answer to Question #140860 in Molecular Physics | Thermodynamics for Cayden

Question

A ball player hits a home run, and the baseball just clears a wall 18.8 m high located 115.0 m from home plate. The ball is hit an an angle of 35° to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 1.0 m above the ground.

(a) What is the initial speed?

 

(b) How much time does it take for the ball to reach the wall?

 

(c) Find the components of the velocity and the speed of the ball when it reaches the wall

Answer 1

a) We use frame of reference wherein $x_0=0$ and $y_0=1 m$

$x-x_0=v_0cos\theta_0t$

$t=\frac{x}{(v_0cos\theta_0)}=\frac{115}{(v_0cos35)}$

$y-y_0=v_0sin\theta_0t+\frac{1}{2}gt^2$

$18.8-1=v_0sin35(\frac{115}{(v_0cos35)})+(-4.9)[\frac{115}{(v_0cos35)]^2}$

$38.81m/s$

b)

$t=\frac{x}{u_x}=\frac{115}{ucos35}=\frac{115}{38.81cos35}=3.41 sec$

c) for horizontal motion;

$v_x=u_x=ucos35\degree=38.1cos35=31.2m/s$

for vertical motion;

$v_y=u_y-gt=usin35\degree-9.8\times3.41$

$=37.81sin35\degree-9.8\times3.4$

$22.7546-35.358$

-13.260m/s