A freight train is moving at a constant speed of Vt. A man standing on a flatcar

Question

A freight train is moving at a constant speed of Vt. A man standing on a flatcar throws a ball into the air and catches it as it falls. Relative to the flatcar, the initial velocity of the ball is Vib straight up.

a. What are the magnitude and direction of the initial velocity of the ball as seen by a second man standing on the ground next to the track?

b. How much time is the ball in the air according to the man on the train? According to the man on the ground? Mathematically prove your two answers.

c. What horizontal distance has the ball traveled by the time it is caught according to the man on the train? According to the man on the ground?

d. What is the minimum speed of the ball during its flight according to the man on the train? According to the man on the ground?

e. What is the acceleration of the ball according to the man on the train? According to the man on the ground?

Please show work. A picture as well would be much appreciated.

Explanation / Answer

a)let i be the direction of the motion of train and j be the vertical direction.velocity of ball relative to man on ground=7i +14.9j=16.46 m/s at 64.84 degrees above the horizontalb) time for ball in air=tut-0.5gt2=0t=3.04 seconds?3 secondsc) Time for which the ball is in the air according to the man on the ground=3 secondsd) since the train is at rest according to the man on the train, horiontal distance covered by the ball=0.e) horizontal distance covered according to man on ground= spee

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