Question

A football quarterback shows off his skill by throwing a pass 45.90 m downfield and into a bucket. The quarterback consistently launches the ball at 40.00 ∘ above horizontal, and the bucket is placed at the same level from which the ball is thrown.
What initial speed is needed so that the ball lands in the bucket?

Answer 1

s = speed

45.9 = u T
where
u = s cos 40
so
T = 45.9 /(s cos 40) where T is time aloft

rise time is half T or t = T/2
v = Vi - g t
Vi = s sin 40
at top v = 0
s sin 40 = 9.81 t = 9.81[45.9/(2s cos 40]
or
2 s^2 sin 40 cos 40 = 9.81*45.9

remember trig now

Answer 2

Similarly, when you solve for m = 46, you get:

2 s^2 sin 40 cos 40 = 9.81*46
s = 21.40 m/s

You're welcome.