Paper 3 Projectile Motion Drills

Q1 Projectile landing below launch level

A rescue package is projected from a platform $25.0\mathrm{m}$ above level ground. Its initial speed is $22.0\mathrm{m}{\mathrm{s}}^{-1}$ at $28.0^{\circ }$ above the horizontal. Air resistance is negligible.

1. Explain why the standard range formula $R=u^2\sin 2\theta /g$ should not be used directly. [2]
2. Calculate the time taken for the package to reach the ground. [4]
3. Calculate the horizontal range from the base of the platform. [2]
4. Calculate the velocity vector just before impact. [4]
5. State one way in which air resistance would change the actual landing point. [2]

Q2 Trajectory equation

A particle is launched from the origin with initial speed $u$ at angle $\theta$ above the horizontal. Air resistance is negligible.

1. Starting from component equations, show that the trajectory can be written as

$$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }.$$

[4] 2. For $u=16.0\mathrm{m}{\mathrm{s}}^{-1}$ and $\theta =40.0^{\circ }$, calculate the height of the projectile when $x=12.0\mathrm{m}$. [3] 3. Explain why the trajectory is parabolic in this model. [2] 4. The same projectile is launched on the Moon where gravitational field strength is smaller. State and explain the effect on the horizontal range for the same $u$ and $\theta$. [3]