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# A quarterback throws a football toward a receiver with a more in details physics!?

A quarterback throws a football toward a receiver with an initial speed of 17 m/s at an angle of 30° above the horizontal. At that instant, the receiver is 20 m from the quarterback. In what direction and with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

____________The receiver should run in the direction the football is travelling.

___________The receiver should run in the direction opposite to that in which the football is travelling.

__________ m/s

### 2 Answers

- Anonymous1 decade agoFavorite Answer
Let:

x be the horizontal distance of the ball from the quarterback at time t.

Resolving horizontally and vertically for the flight of the ball:

x = 17t cos(30) ...(1)

0 = 17t sin(30) - 9.81t^2 / 2 ...(2)

(2) gives:

t(17 sin(30) - 9.81t / 2) = 0

t = 0 (initially)

or (when the ball returns to the same level):

t = 17 sin(30) * 2 / 9.81

= 17 / 9.81

= 1.73 s.

Substituting for t in (1):

x = 17^2 sqrt(3) / (9.81 * 2)

= 25.5 m.

The receiver needs to run in the opposite direction at

5.5 / 1.73

= 3.18 m/s.