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 attained by the body is

Options

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

Answer

D

Explanation

`x=10sqrt(3)t, y=10t-t^(2), (dx)/(dt)=10sqrt(3)`
`v_(y)=(dy)/(dt)=10-2trArr at t=5`sec
`v_(y)` becomes zero at maximum height
`rArr y=10xx5-5^(2)=25 m`.