A ball A is thrown vertically upwards with speed u. At the same instant another ball B is released from rest height h. At times t, the speed of A relative to B is :-
Question
A ball A is thrown vertically upwards with speed u. At the same instant another ball B is released from rest height h. At times t, the speed of A relative to B is :-
Solution
To solve this problem, we need to understand the relative motion of the two balls A and B.
Step 1: Determine the velocity of each ball at time t.
For ball A, which is thrown upwards with initial speed u, the velocity at time t (vA) can be calculated using the equation of motion: v = u - gt. Here, g is the acceleration due to gravity.
For ball B, which is released from rest, the velocity at time t (vB) can be calculated using the equation of motion: v = gt.
Step 2: Determine the relative velocity of A with respect to B.
The relative velocity of A with respect to B (vAB) is the difference between the velocities of A and B. So, vAB = vA - vB.
Substituting the expressions for vA and vB from step 1, we get:
vAB = (u - gt) - (gt) = u - 2gt.
So, the speed of A relative to B at time t is u - 2gt.
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