a) At what angle above the horizontal was the ball thrown if its initial speed was 15m/s, assuming the smaller of the two possible angles was used?

Question

A rugby player passes a ball 8m8m across a field to a teammate, where it is caught at the same height as it left his hand. Treat the effect of air resistance to be negligible. Include units as appropriate below.

a) At what angle above the horizontal was the ball thrown if its initial speed was 15m/s15m/s, assuming the smaller of the two possible angles was used?

(b) What other angle above the horizontal would give the same range?

(c) Determine the difference in flight times between these two trajectories. What is this value?

Answer 1

R = V0^2 sin(2u) /g

Note that this range equation ONLY works when the object lands at the same height as it is launched.

8 = 15^2 sin(2u) / 9.8

sin (2u) = 0.348

2u = 20.4 or 159.6 Note that the two solutions are supplementary angles because sin u = sin (180-u).

u = 10.2 or 79.8

Time of flight = 2 * time to reach the highest point

= 2 * V0 sin u / g

= 0.542 or 3.013

3.013 - 0.542 = 2.47 s