A heavy stone is thrown from a cliff of height h in a given direction. The speed with which it hits the ground
(a) must depend on the speed of projection
(b) must be larger than the speed of projection
(c) must be independent of the speed of projection
(d) may be smaller than the speed of projection.
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(a) must depend on the speed of projection
(b) must be larger than the speed of projection
Explanation:
Since Kinetic Energy given to the stone is dependent on the speed of projection, and the speed with which it hits the ground is dependent upon the K.E. given to the stone at the time of projection, Hence answer (a).
When the stone hits the ground its K.E. is the sum of K.E. given to it at the time of projection and the Potential energy at the point of projection with respect to the ground. That means K.E. of the stone is more at the ground than the point of projection. Since K.E. of a given mass particle is only dependent on its speed, so its speed when it hits the ground must be larger than the speed of projection. Hence (b). (c) and (d) are opposite to the above condition, hence not true.