a ball player hits a home run and the baseball just clears a wall 8 m high located 146.1 m from home plate?

Question

the ball is hit at an angle of 37.3 degrees to the horizontal, and air resistance is negligible. assume the ball is hit at a height of 1.1 m above the ground.
a) what is the initial speed of the ball? Answer in units of m/s.
b) How much time does it take for the ball to reach the wall? Answer in units of s.
c) Find the speed of the ball when it reaches the wall. Answer in units of m/s.

Answer 1

The equations of motion are
y(t)=1.1+v0*sin(37.3)*t-.5*9.8*t^2

x(t)=v0*cos(37.3)*t

when x(t)=146.1 and y(t)=8, the ball clears the wall

using x(t)
v0*t=146.1/cos(37.3)
=183.7
now use that is y(t)
8=1.1+183.7*sin(37.3)-.5*g*t^2

solve for t, which is the flight time
t=4.616 seconds

now solve for v0
39.79 m/s


vy=v0*sin(37.3)-9.8*t
vy=-21.12 m/s

vx=v0*cos(37.3)
vx=31.65 m/s

v=sqrt(vx^2+vy^2)
v=50.84 m/s

j

Answer 2

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