Question

Two soccer players start from rest, 50 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 0.48 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 * 0.48* t^2 = 0.24 t^2

As they collide, the sum of their distances travelled = 50 m

=> 0.20 t^2 + 0.24 t^2 = 50

=> 0.44 t^2 = 50

=> t^2 = 50 / 0.44 = 113.6364

=> t = 10.66 secs.

Players collide after 10.66 secs (ANSWER).

b.

First player’s distance travelled = 0.20 * 113.6364 = 22.73 m .

Hence,  at the instant they collide, first player has run = 22.73 m (ANSWER).