Question

In a football game, one team kicks off to the other. At the moment the receiver catches the ball, he is 40 meters from the nearest tackler. The receiver runs left to right at a speed of 10 meters per second (10 m/s). The tackler runs right to left at a speed of 6 meters per second.

How long does it take before they collide? ___________

How far does the receiver go? _____________________

Answer 1

Take left to be the negative direction, and right to be positive.

The receiver's position at time t, taking his starting position to be the origin, is

(10 m/s) t

while the tackler's position is

40 m + (-6 m/s) t

The two collide when their positions are equal:

(10 m/s) t = 40 m - (6 m/s) t

(16 m/s) t = 40 m

t = (40 m) / (16 m/s)

t = 2.5 s

In this time, the receiver covers a distance of

(10 m/s) (2.5 s) = 25 m