At a football game, at the instant the ball goes into play, a player at the line of scrimmage begins running along the edge of the field at a rate of 25 ft/sec. The quarterback receives the ball and is forced into position 30 feet across the field from the boundary line along which the player is running, and 2.5 feet behind the line of scrimmage. 1.5 seconds later, the quarterback is poised to throw the ball. At that instant, what is the rate at which the distance is changing from the quarterback to the player?

Question

Please help I know u need to use the Pythagorean Therom but am not sure how to solve. I know the answer is 20.

Answer 1

let the distance run by the running player be x from the line of scrimmage.
Let the distance between them be d

In my diagram, I have a right-angles triangle with fixed side of 30, the other side (x+2.5) and the hypotenuse d, so that

d^2 = (x+2.5)^2 + 30^2
2d dd/dt = 2(x+2.5) dx/dt
when t = 1.5, x = 37.5 and
d^2 = (40)^2 + 30^2
d = 50
2(50) dd/dt = 2(40)(25)
dd/dt = 80(24)/100 = 19.2 ft/sec

check my arithmetic

Answer 2

shouldnt it be 25 for the last line, not 24? all else looks right tho