OCR MEI M1 2014 June — Question 4

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2014
SessionJune
TopicProjectiles

4 Fig. 4 illustrates a situation in which a film is being made. A cannon is fired from the top of a vertical cliff towards a ship out at sea. The director wants the cannon ball to fall just short of the ship so that it appears to be a near-miss. There are actors on the ship so it is important that it is not hit by mistake. The cannon ball is fired from a height 75 m above the sea with an initial velocity of \(20 \mathrm {~ms} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal. The ship is 90 m from the bottom of the cliff. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63a2dc41-5e8b-4275-8653-ece5067c4306-3_337_1242_1717_406} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. The director calculates where the cannon ball will hit the sea, using the standard projectile model and taking the value of \(g\) to be \(10 \mathrm {~ms} ^ { - 2 }\). Verify that according to this model the cannon ball is in the air for 5 seconds. Show that it hits the water less than 5 m from the ship.
  2. Without doing any further calculations state, with a brief reason, whether the cannon ball would be predicted to travel further from the cliff if the value of \(g\) were taken to be \(9.8 \mathrm {~ms} ^ { - 2 }\).