Today I give you a free response practice question on kinematics. I’ll give you the answer in my next post.

A ball at a height *H* is released from rest at the instant *t =* 0 and it strikes a fixed touch plate P, inclined at 45º with respect to the vertical, at the instant *t* = *t*_{1}. The point where the ball strikes the plate is at a height *h* (fig.). The collision between the ball and the plate is elastic. After the collision the ball continues its motion and strikes the ground at the instant *t* = *t*_{2}. Now, answer the following questions:

(a) If the height *h* where the ball strikes the plate is varied, how will you indicate, graphically, the variation of *t*_{1} with (*H* – *h*)? Use the coordinate axes as shown in the figure below to show the nature of variation.

(b) After the collision what is the nature of the path followed by the ball? Pick out your answer from the following three options by putting a tick (√) mark against the correct one:

Straight line path ……

Parabolic path ……

Arc of a circle …..

Justify your answer.

(c) Derive an expression for the total time of flight* * *t*_{2} of the ball.

(d) Determine the horizontal displacement of the ball when it strikes the ground.

* AP Physics C* aspirants should answer the following part also:

(e) For a given value of *H* determine the value of *h *for which the time of flight *t*_{2} of the ball is *maximum*.

Try to answer the above question. I’ll be back soon with a model answer for your benefit.

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