Paper 4 Projectile Motion Drills

Q1 Horizontal range investigation

A student launches a small ball horizontally from a bench using the same launcher setting each time. The bench height $h$ above the floor is varied. The horizontal range $x$ is measured.

For horizontal launch,

$$x=u\sqrt{\frac{2h}{g}}.$$

1. Show that a graph of $x^2$ against $h$ should be linear. [2]
2. State how the launch speed $u$ can be found from the gradient. [2]
3. Suggest how the student should measure the landing position to reduce random error. [2]
4. Explain why the same launcher setting should be used for all readings. [1]
5. State one safety precaution for this experiment. [1]

Q2 Video analysis of a projectile

The vertical positions of a ball launched upward are measured from video frames. Upward is positive.

$t/\mathrm{s}$	0.00	0.10	0.20	0.30	0.40	0.50
$y/\mathrm{m}$	0.000	0.244	0.390	0.438	0.388	0.240

1. Starting from $y=u_{y}t-\frac{1}{2}g{t}^2$, show that for $t>0$,

$$\frac{y}{t}=u_y-\frac{1}{2}gt.$$

Explain why plotting $y/t$ against $t$ gives a straight line. [3] 2. Calculate $y/t$ for the five non-zero times. [2] 3. Plot $y/t$ against $t$ on the grid below and draw a straight line of best fit. [5]

4. Use the gradient to determine $g$. [3]
5. Suggest one source of systematic error in the video analysis and state how it affects the measurements. [2]