The motor in a toy rocket expels gases straight downwards, and as a result the rocket accelerates vertically upwards from the ground. The rocket begins moving from rest at time $t = 0$. Figure 2.1 shows how the vertical velocity $v$ of the rocket varies with time $t$ during the first $0.30\,\text{s}$ of the flight. As the rocket travels, the thrust force $T$ produced by the rocket engine is $16\,\text{N}$. For this part of the motion, assume that the rocket’s mass remains constant. Assume also that air resistance is negligible.
(a(i))[1]
Show that the rocket's acceleration is $55\,\text{m s}^{-2}$.
(a(ii))[1]
State an expression for the resultant force $F$ on the rocket in terms of the thrust force $T$ and the weight $W$ of the rocket.
(a(iii))[2]
Calculate the rocket's mass.
(b(i))[2]
At time $t = 0.30\,\text{s}$, a small piece of metal detaches from the rocket. Calculate the height of the rocket above the ground at $t = 0.30\,\text{s}$.
(b(ii))[3]
Calculate the speed with which the piece of metal hits the ground.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Acceleration found as $a = \dfrac{16.5 - 0}{0.30 - 0} = 55\,\text{m s}^{-2}$” …