A football is thrown toward a receiver with
an initial speed of 16.6 m/s at an angle of
35.3
◦
above the horizontal. At that instant,
the receiver is 15.4 m from the quarterback.
The acceleration of gravity is 9.81 m/s
2
.
With what constant speed should the receiver run to catch the football at the level at
which it was thrown?
Answer in units of m/s.
initial speed up = Vi = 16.6 sin 35.3
v = Vi - g t
v = 0 at top
so at top
t = Vi/g = (16.6 sin 35.3) / 9.81 = 0.978 second to top
so 2 * 0.978 = 1.96 seconds in air
How far did it go horizontal?
1.96 seconds * 16.6 cos 35.3 = 26.6 meters
so the catcher assuming he ran straight downfield from the quarterback has to go 26.6 - 15.4 = 11.2 meters in 1.96 seconds
= 11.2 / 1.96 = 5.71 m/s