Question

A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is thrown 

(a) vertically downward 

(b) vertically upward 

(c) horizontally 

(d) the speed does not depend on the initial direction.

Answer 1

(d) the speed does not depend on the initial direction.

Explanation:- 

When the stone is thrown its total mechanical energy = K.E.+P.E. 

= ½mv² + mgh ---------(i) 

This energy is conserved and when near the ground its P.E. is also converted to K.E. because of h=0. suppose it hits the ground with speed v', its total energy 

= ½mv'² -----(ii) 

equating (i) and (ii) we get,

 ½mv'²=½mv²+mgh v'²=v²+2gh 

Clearly v' depends only on the value of v whatever be the initial direction.