Speed of A with respect to B is 'u'
i dont know correctly,i did something and got answer 'u'
am i right??

Analysis

To analyze the situation, let's consider the motion of ball A and ball B separately.

Motion of Ball A

Ball A is thrown vertically upward with speed u. Due to gravity, it will experience a downward acceleration of g (acceleration due to gravity). The initial velocity of A is u, and the final velocity at time t will be vA.

Using the equation of motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the final velocity of ball A at time t:

vA = u - gt

Motion of Ball B

Ball B is released from rest at height h. It falls freely under the influence of gravity. The initial velocity of B is 0, and the final velocity at time t will be vB.

Using the equation of motion v = u + at, we can calculate the final velocity of ball B at time t:

vB = 0 + gt

Speed of A relative to B

To find the speed of A relative to B at time t, we need to calculate the difference between the velocities of A and B. The speed of A relative to B is given by:

Speed of A relative to B = vA - vB

Substituting the values of vA and vB, we get:

Speed of A relative to B = (u - gt) - (0 + gt)
= u - gt - gt
= u - 2gt

So, the speed of ball A relative to ball B at time t is u - 2gt.

Summary

- Ball A is thrown vertically upward with speed u, while ball B is released from rest at height h.
- Ball A experiences a downward acceleration due to gravity, while ball B falls freely under gravity.
- The final velocity of ball A at time t is vA = u - gt, where g is the acceleration due to gravity.
- The final velocity of ball B at time t is vB = gt.
- The speed of A relative to B at time t is given by the difference between their velocities: Speed of A relative to B = vA - vB = (u - gt) - (0 + gt) = u - 2gt.