A man standing atop a car traveling at 25m/s throws a ball in the opposite direc

Question

A man standing atop a car traveling at 25m/s throws a ball in the opposite direction of motion of the car with a velocity of 18 m/s. What is the velocity of the ball from the perspective of an observer at rest? Then, if the man throws the ball in the same direction as the car’s motion, what then would be the velocity of the ball from the POV of an observer at rest?

So I think the answers are 7m/s and 43m/s respectively, but I'm not really sure on how to explain/justify this? If you could please give a detailed explaination so I could learn for next time, that would be much appreciated!! Thank you so much! :)

Explanation / Answer

aps the easy way is to consider movement of i ball A relative to ii man in/on car B. (as if B were at rest and only A moving)

for a neutral observer at rest let the direction of the car be the positive x-axis direction.

v - v = - 18 m/s (relative to the person on the car as if she or he were at rest)
v = 25 m/s (relative to a stationary observer (neutral observer))

[please note: if the the velocities of objects A and B are v and v with respect to a stationary observer (neutral observer) on the ground surface, then the velocity of A relative to B is v - v. this is as if B were at rest and only A were moving.]

we need to calculate v (velocity of the ball (relative to a stationary observer (neutral observer))

v - v = - 18 m/s => v - 25 = - 18

=> v = 25 - 18 = 7 m/s


b) if the ball is projected in the same direction as the car

=> v - v = + 18 m/s

=> v = 18 + 25 = 43 m/s

Ans:

velocity of the ball from the perspective of an observer at rest
a) 7 m/s (in the car movement direction)
b) 43 m/s (in the car movement direction)

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