A freight train is moving at a constant speed of 7 m/s. A man standing on a flat

Question

A freight train is moving at a constant speed of 7 m/s. 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 14.9 m/s straight up.

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

b.) How long is the ball in the air according to the man on the train?

c.)How long is the ball in the air according to the man on the ground?

d.) What horizontal distance has the ball traveled by the time it is caught according to the man on the train?

e.)What horizontal distance has the ball traveled by the time it is caught according to the man on the ground?

f.) What is the minimum speed of the ball during its flight according to the man on the train?

g.) What is the minimum speed of the ball during its flight according to the man on the ground?

h.) What is the acceleration of the ball according to the man on the train?

i.) What is the acceleration of the ball according to the man on the ground?

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 horizontal

b) time for ball in air=t

ut-0.5gt2=0

t=3.04 seconds3 seconds

c) Time for which the ball is in the air according to the man on the ground=3 seconds

d) 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= speed of train*time for ball to fall back=7*3=21m

f) the minimum speed in flight according to man on train is achieved at the topmost point and is 0.

g)the minimum speed of the ball during its flight according to the man on the ground is also achieved at the topmost poinr but equals the velocity of the train=7m/s

h)the acceleration of the ball according to the man on the train=9.8 m/s2

i)the acceleration of the ball according to the man on the ground=9.8 m/s2

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