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?
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).
Two soccer players start from rest, 34 m apart. They run directly toward each other, both...
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