A stone of mass 2 kg is projected upward with kinetic energy of 98 J. The height at which the kinetic energy of the stone becomes half its original value, is given by

A stone of mass 2 kg is projected upward with kinetic energy of 98 J.

1.	A stone of mass 2 kg is projected upward with kinetic energy of 98 J. The height at which the kinetic energy of the stone becomes half its original value, is given by
Answer» 5 m 2.5 m 1.5 m 0.5 m Solution :At the time of PROJECTION KINETIC ENERGY of the stone, `K= 1/2m U^2` where m is the mass of the stone and u is the velocity of the projection. or `mu^2 = (2K)/(m) = (2 xx 98)/(2) = 98` Let h be the maximum height attained by the stone. `:. h = (u^2)/(2g) or h = (98)/(2 xx 9.8) = 5 m "" .....(i)` Also, `K = 1/2 m (2gh) "" `(Using (i)) Let h. be the height at which the kinetic energy of hte stone becomes half. `:. K. = 1/2 m (2 gh.)` `:. (K.)/K = (h.)/h ` But `K. = K/2 :. K/(2K) = (h.)/(h)` or `h. = h/2 = 5/2 m = 2.5 m`.