A quarterback throws a football toward a re- ceiver with an initial speed of 25 m/s, at an angle of 35◦ above the horizontal. At that instant, the receiver is 20 m from the quarter- back.
With what constant speed should the re- ceiver run in order to catch the football at the level at which it was thrown? The accelera- tion of gravity is 9.8 m/s2 .
Answer in units of m/s
With what constant speed should the re- ceiver run in order to catch the football at the level at which it was thrown? The accelera- tion of gravity is 9.8 m/s2 .
Answer in units of m/s
-
football vertical speed = 25 sin 35 = 14.34 m/s
football horizontal speed = 25 cos 35 = 20.48 m/s
Time football in the air:
t = 2 v/a = 2 x 14.34 / 9.8 = 2.93 sec
distance the football to be catch:
s = t x v = 2.93 x 20.48 = 60.01 m
The receiver is 20m from the quarterback, so he will have to run 60.01 - 20 = 40.01 m, for 2.93 sec.
His speed must be:
V = s/t = 40.01 / 2.93 = 13.66 m/sec
football horizontal speed = 25 cos 35 = 20.48 m/s
Time football in the air:
t = 2 v/a = 2 x 14.34 / 9.8 = 2.93 sec
distance the football to be catch:
s = t x v = 2.93 x 20.48 = 60.01 m
The receiver is 20m from the quarterback, so he will have to run 60.01 - 20 = 40.01 m, for 2.93 sec.
His speed must be:
V = s/t = 40.01 / 2.93 = 13.66 m/sec