A football is kicked with an initial speed of 63 ft/s at a an angle of 45 degrees. A receiver on the goal line 69 yd away in the direction of the kick starts running to meet the ball at that instant.

Question

What must be his minimum speed (in feet/second) if he is to catch the ball before it hits the ground?

Answer 1

The initial vertical speed will be 63 sin 45, and initial horizontal speed 63 cos 45

Using s = ut + 0.5 at², the ball will be on the ground when s = 0 (s = vertical distance above ground)

so t = 0, or u + 0.5 at = 0, a = -32 ft/s/s so 63 sin 45 - 16 t = 0 so t = 63 sin 45 / 16.

In that time the ball will have moved horizontally 63 cos 45 x 63 sin 45 / 16 feet.

The receiver starts 69 x 3 ft = 207 ft from the kicker

So if v is his minimum speed , v (63 sin 45 / 16) > 207 - (63 cos 45 x 63 sin 45) / 16

Rearranging, v > 29.8 feet per second

Mike