6 A ball is hit from horizontal ground with velocity \(( 10 \mathbf { i } + 24.5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) where the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal and vertically upwards respectively.
- State two assumptions that you should make about the ball in order to make predictions about its motion.
- The path of the ball is shown in the diagram.
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- Show that the time of flight of the ball is 5 seconds.
- Find the range of the ball.
- In fact the ball hits a vertical wall that is 20 metres from the initial position of the ball.
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Find the height of the ball when it hits the wall. - If a heavier ball were projected in the same way, would your answers to part (b) of this question change? Explain why.