AQA M1 2012 January — Question 8

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2012
SessionJanuary
TopicProjectiles

8 A girl stands at the edge of a quay and sees a tin can floating in the water. The water level is 5 metres below the top of the quay and the can is at a horizontal distance of 10 metres from the quay, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{d42b2e88-74ea-486b-bb47-f512eb0c185d-6_428_899_482_575} The girl decides to throw a stone at the can. She throws the stone from a height of 1 metre above the top of the quay. The initial velocity of the stone is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) below the horizontal, so that the initial velocity of the stone is directed at the can, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{d42b2e88-74ea-486b-bb47-f512eb0c185d-6_437_903_1238_571} Assume that the stone is a particle and that it experiences no air resistance as it moves.
  1. Find \(\alpha\).
  2. Find the time that it takes for the stone to reach the level of the water.
  3. Find the distance between the stone and the can when the stone hits the water.