{harder }

full solutions (either when someone gets it, or next week):

in the diagram, a large number of projectiles are fired simultaneously from o, each with the same velocity v m/s, but different angles of projection theta, at a wall d metres from o. the projectiles are fired so they all lie in the same vertical plane perpendicular to the wall.

you may assume that the equations of motion at time t are given by:
and .

i) using these two equations of motion, prove the relationship between the height y and time t is:

ii) show that the first impact at the wall occurs at time and that this projectile was fired horizontally.

iii) hence, find where this projectile hits the wall.

iv) show that for , there are two impacts at time t, and that the distance between these is:

.

v) given that v = 10 m/s and d = 10 metres, what are the initial angles of projection of the two projectiles that will strike the wall simultaneously metres apart.