Question

Two football players separated by a distance of 42m run directly toward each other. Football

player 1 starts from rest and accelerates at 2.4m/s/s, and football player 2 moves with a
uniform velocity of 5.4m/s.
for road
a. If the two players begin running at the exact same instant, how long does it take the
two players to collide?

Answer 1

To find out how long it takes for the two football players to collide, we need to determine the time it takes for player 1 to catch up to player 2.
First, let's calculate the time it takes for player 1 to reach player 2.
We can use the formula:
distance = initial velocity × time + 0.5 x acceleration × time ^2
Since player 1 starts from rest (initial
velocity = 0) and accelerates at a rate of
2.4m/s ^2, we can rearrange the formula as follows:
42m = 0 × time + 0.5 × 2.4m/s^2 × time^2
Simplifying the equation gives us:
42m = 1.2m/s^2 × time^2
Dividing both sides of the equation by 1.2m/s^2 gives:
35s^2 = time^2
Taking the square root of both sides

time = V35s = 5.92s
So, it takes player 1 approximately 5.92 seconds to reach player 2.
Now, let's calculate the time it takes for player 2 to reach player 1.
Player 2 moves with a uniform velocity of 5.4m/s. Since the players are separated by a distance of 42m, we can use the formula:
time = distance / velocity
time = 42m / 5.4m/s = 7.78s
Therefore, it takes player 2 approximately 7.78 seconds to reach player 1.
Since we're looking for the time it takes for the two players to collide after starting running at the same instant, we take the longer time, which is approximately 7.78 seconds.
Therefore, it takes approximately 7.78 seconds for the two football players to collide.