Projectile Motion (OCR AS Physics): Revision Note

To calculate vertical projection (free fall)

A science museum designed an experiment to show the fall of a feather in a vertical glass vacuum tube.

The time of fall from rest is 0.5 s.

What is the length of the tube, L?

Answer:

Step 1: List the known quantities

• Length of the tube, $s=L$

• Initial velocity, $u=50\mathrm{m}{\mathrm{s}}^{-1}$

• Acceleration, $a=9.81\mathrm{m}{\mathrm{s}}^{-2}$

• Time, $t=0.5\mathrm{s}$

Step 2: Choose the equation which contains the quantities listed in Step 1

• The equation that links $s$, $u$, $a$ and $t$ is

$s=ut+\frac{1}{2}a{t}^2$

Step 3: Calculate the length

$L=0\times 0.5+\frac{1}{2}\times 9.8\times 0.5^2$

$L=1.2\mathrm{m}$

To calculate horizontal projection

A motorcycle stunt-rider moving horizontally takes off from a point 1.25 m above the ground, landing 10 m away as shown.

What was the speed at take-off?

Answer:

Step 1: Consider the vertical motion first and list the known quantities:

• Height, $s=1.25\mathrm{m}$

• Initial velocity, $u=0$

• Acceleration, $a=9.81\mathrm{m}{\mathrm{s}}^{-2}$

• Time of flight, $t$

Step 2: Calculate the time of flight using the quantities listed in Step 1

• The equation that links $s$, $u$, $a$ and $t$ is

$s=ut+\frac{1}{2}a{t}^2$

$s=\frac{1}{2}a{t}^2$

$t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2\times 1.25}{9.81}}=0.505\mathrm{s}$

Step 3: Consider the horizontal motion and list the known quantities:

• Distance travelled, $s=10\mathrm{m}$

• Initial velocity, $u$

• Acceleration, $a=0$

• Time of flight, $t=0.505\mathrm{s}$

Step 4: Calculate the speed at take-off

• Since the acceleration is zero, use the following equation

$\mathrm{velocity}=\frac{\mathrm{displacement}}{\mathrm{time}}$

$u=\frac{10}{0.505}$

$u=19.8\mathrm{m}{\mathrm{s}}^{-1}$

Make sure you don’t make these common mistakes:

• Forgetting that the acceleration is negative (−9.81 m s^-2 if upwards is positive) as the object rises

• Confusing the direction of sin θ and cos θ

• Not converting units (mm, cm, km etc.) to metres