A body is projected at time `t = 0` from a certain point on a planet's surface with a certain velocity at a certain angle with the planet's surface (assumed horizontal). The horizontal and vertical displacement x and y (in metre) respectively vary with time t in second as, `x= (10sqrt(3)) t and y= 10t - t^2`. The maximum height in meter attained by the body is

Options

A. 100 m
B. 75 m
C. 50 m
D. 25 m.

Answer

D

Explanation

`(y_(max))implies(dy)/(dt)=0`
`implies (d)/(dt)(10 t-t^(2))= 10 - 2t" "implies t= 5`
`implies" "y underset(max)"=10(5)-5^(2)=25 m`