Question

Two soccer players start from rest, 42 m apart. They run directly toward each other, both players accelerating. The first player’s acceleration has a magnitude of 0.60 m/s 2. The second player’s acceleration has a magnitude of 0.45 m/s2. (a) How much time passes before the players collide

Answer 1

8.94 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

`s=ut+(1)/(2)at^2\\\Rightarrow s_1=0t+(1)/(2)* 0.6* t^2\\\Rightarrow s_1=0.3t^2`

`s=ut+(1)/(2)at^2\\\Rightarrow s_2=0t+(1)/(2)* 0.45* t^2\\\Rightarrow s_2=0.225t^2`

They both will run for the same amount of time assuming that they started running at the same time and together they will travel 42 m.

`42=0.3t^2+0.225t^2\\\Rightarrow t=\sqrt{(42)/(0.3+0.225)}\\\Rightarrow t=8.94\ s`

The time at which they will collide is 8.94 seconds