A science student is riding on a flatcar of a train traveling along a straight horizontal track at a constant speed of 10.5 m/s. The student throws a ball into the air along a path that he judges to make an initial angle of 69.0° with the horizontal and to be in line with the track. The student's professor, who is standing on the ground nearby, observes the ball to rise vertically. How high does she see the ball rise?

Height as seen by the professor = 38.2 m

Explanation:

Angle of throw = θ = 69°

Velocity of throw = v

X component of velocity = v₁ = v cos 69 = 0.3584 v m/s

Vertical component of the velocity = v₂ = v sin 69 = 0.9336 v m/s

v₂ / v₁ = tan 69 = 2.605

v₂ = 2.605 v₁.

Professor sees as if the x component of velocity = 0

v (as seen by professor) + v' = 0

=> v as seen by professor = - v' = - 10.5 m/s

This shows that y component of the ball's velocity is 2.605 times its x component of velocity.

with respect to the professor, there is only y component of velocity.

v₂' = v₂ = 2.605 (-10.5) = 27.4 m/s.

Height as seen by the professor = (27.4) ² / 2 (9.8) = 38.2 m