Physics 9702 · AS & A Level · Equations of motion

Equations of motion — practice question

A ball is launched horizontally at $41.0\,\text{m s}^{-1}$ from a cannon that is at rest on the top of a hill. It hits horizontal ground a vertical distance of $57\,\text{m}$ below the cannon, as shown in Fig. 3.1. Take air resistance as negligible.
(a)[2]

Show that, after being fired, the ball takes $3.4\,\text{s}$ to reach the ground.

(b)[1]

Calculate how far horizontally the ball is from the cannon when it lands on the ground.

(c)[2]

Determine the magnitude of the ball’s displacement from the cannon when it lands on the ground.

(d)[1]

The ball leaves the cannon at time $t = 0$. On Fig. 3.2, sketch a graph to show how the magnitude $v$ of the vertical component of the velocity of the ball varies with time $t$ from $t = 0$ to $t = 3.4\,\text{s}$. Numerical values are not required.

(e)[2]

When the cannon fires the ball, it recoils horizontally at $0.340\,\text{m s}^{-1}$. The combined mass of the ball and the cannon is $1480\,\text{kg}$. Assume that there are no external horizontal forces on the ball-cannon system. Determine, to three significant figures, the mass of the ball.

(f)[2]

The cannon now fires a ball with a smaller mass. Assume that air resistance remains negligible. State and explain any change to the graph in Fig. 3.2 that is caused by the smaller mass of the ball.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $s = \tfrac{1}{2}at^2$

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