A balloon starts ascending from the ground at a constant speed of `25 m//s`. After 5 s, a bullet is shot vertically upwards from the ground.
(i) What should be the minimun speed of the bullet so that it may reach the balloon?
(ii) The bullet is shot at twise the speed calculated in (i). Find the height at which it passes the balloon.

Answer

`75 ms^(-1), (437.5 +- 62.5 sqrt(21))m`

Explanation

`-25 m//s` After 5 sec
height of balloon `= 25 xx 5 = 125 m`
(i) Minimum speed
`125 = ((u -25)^(2))/(2g) rArr (u -25)^(2)=2500`,
`u-25 =50 , u = 75 m//s`
(ii) `u = 2 xx 75 = 150 m//s`
`125 = (150 - 25)t - 5 t^(2)`
`125 = 125 t - 5t^(2) rArr t^(2) - 25 t + 25 = 0`.