A rocket is fired vertically up from the ground with a resultant vertical acceleration of `10 m//s^2.` The fuel is finished in 1 min and it continues to move up. (a) What is the maximum height reached? (b) Afte2r how much time from then will the maximum height be reached?(Take `g= 10 m//s^2`)

Explanation

Let the passenger catch the bus after time t.
The distance travelled by the bus, `" "s_(1)=0+1/2 at^(2)` …(i)
and the distance travelled by the passenger `" "s_(2)=ut+0` …(ii)
Now the passenger will catch the bus if `d+s_(1)=s_(2)` ...(iii)
`rArr d+1/2 at^(2)=ut rArr 1/2 at^(2)-ut+d=0rArr t=([u+-sqrt(u^(2)-2ad)])/a`
so the passenger will catch the bus if t is real, i.e., `u^(2) ge 2ad rArr u^(2) ge u^(2)sqrt(2ad)`
So the minimum speed of passenger for catching the bus is `sqrt(2ad)`.