What are the total time and displacement if the traveler on a train throw ball on level track...

Question:

What are the total time and displacement if the traveler on a train throw ball on level track straight up relative to the train with a speed of 4.90 m/s and velocity of 20.0 m/s?

Projectile motion

The motion of an object purely under the influence of gravity is known as projectile motion. In such motion, the path traced is parabolic. Not only the gravitational field but any other field which is independent of the motion of the object will also show the projectile motion.

With reference to train, the ball went up vertically and the time it will take to get back is twice the time it will take to reach the highest point. Therefore,

{eq}\begin{align*} &T_{1/2}=\frac{20}{9.8}\\ \Rightarrow & T_{1/2}= 2.0408\ s \end{align*} {/eq}

Hence, the total time will be

{eq}\begin{align*} T= 4.0816\ s \end{align*} {/eq}

As the train was moving in horizontal direction, the ball would also have the same velocity as of train. Therefore, the horizontal displacement with reference to an observer on the ground will be

{eq}\begin{align*} &s = vT\\ \Rightarrow & s = 20\ m \end{align*} {/eq}

Conclusion

The total time is 4.0816 seconds and the displacement is 20 meters.