A ball is hit from horizontal ground with velocity $(10i+24\mathrm{.}5j)m{s}^{-1}$ where the unit vectors i and $j$ are horizontal and vertically upwards respectively.

$($a$)$ State two assumptions that you should make about the ball in order to make predictions about its motion.

$($i$)$ Show that the time of flight of the ball is $5$ seconds.

$($ii$)$ Find the range of the ball.

$($c$)$ In fact the ball hits a vertical wall that is $20$ metres from the initial position of the ball.

$($d$)$

$($e$)$

Find the height of the ball when it hits the wall.

$($d$)$ If a heavier ball were projected in the same way, would your answers to part $($b$)$ of this question change? Explain why.