Question

A rocket with a total mass of `20 kg` will take off with an acceleration of `12 ms^-2` if it is launched so that its trajectory is vertically upward. a) Calculate the force produced by the rocket engine? (please check below for part b)

b) The rocket is launched instead pointing at an angle so that its trajectory is a horizontal line. What then will its acceleration be?

(Assume that the rocket engine produces a constant force and that the mass of the
burnt fuel ejected is negligible.)

Answer 1

(a) Net force acting on the rocket

`F_"net"=ma_"net"`
where `m` is mass of rocket.

If `F_p` is the force produced by the rocket, force equation of the takeoff of rocket is

`F_p-mg=ma_"net"`

Rearranging, taking acceleration due to gravity `g=10\ ms^-2` and inserting given values

`F_p=m(a_"net"+g)`
`=>F_p=20(12+10)`
`=>F_p=440\ N`

(b) Let us assume that the rocket is launched so that it has constant acceleration `a_h` in the horizontal direction. Taking this to be direction of positive `x`-axis, net acceleration `=a_hhati`
If `veca_l` is the launch acceleration then force equation becomes

`mveca_l-mghatj=ma_hhati`
where `ghatj` acts in the `-y` direction.
`=>veca_l=ghatj+a_hhati`