A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 `m//s`. To give an initial upward acceleration of 20 `m//s^(2)`, the amount of gas ejected per second to supply the needed thrust will be (Take `g = 10 m//s^(2)`)

Options

A. `187.5 kg //s`
B. `157 .5 kg //s`
C. `137.5 kg //s`
D. `127.5 kg //s`

Answer

A

Explanation

Here ` ,m = 5000 kg , u = 800 m//s (dm )/(dt)=?`
`A= 20 m//s^2 ,g = 10 m//s^2`
Thrust `= m (a +g ) = u (dm )/( dt)`
` therefore (dm )/( dt ) = (m ( a+g))/( u ) = ( 5000 ( 20+10 ))/( 800 ) = ( 1500 )/( 8) = 187.5 kg //s`