Question

Two soccer players start from rest, 34 m apart. They run directly toward each other, both players accelerating. The first player’s acceleration has a magnitude of 0.40 m/s2. The second player’s acceleration has a magnitude of 0.50 m/s2. (a) How much time passes before the players collide? (b) At the instant they collide, how far has the first player run?

Answer 1

Answer 2

SOLUTION :

a.

Let they collide after t secs. 

So,

As the both start from the rest :

Distance travelled by first player = 1/2 a t^2 = 1/2 * 0.40 * t^2 = 0.20 t^2

Distance travelled by second payer = 1/2 a’ t^2 = 1/2 * 0.50* t^2 = 0.25^2

As they collide, the sum of their distances travelled = 34 m

=> 0.20 t^2 + 0.25 t^2 = 34

=> 0.45 t^2 = 34

=> t^2 = 34 / 0.45 = 75.5556

=> t = 8.69 secs.

Players collide after 8.69 secs (ANSWER).

b.

First player’s distance travelled = 0.20 * 75.5556 = 15.11 m .

Hence,  they collide at a  point 15.11 m  from the starting point of the first player. (ANSWER).