Question

During a football game, Igor is 8.0 m behind Brian and is running at 7.0 m/ s when Brian catches the ball and starts to accelerate away at 2.8 m/ s 2 from rest. a) Will Igor catch Brian? If so, after how long?

Answer 1

To determine whether Igor will catch Brian, we need to compare their distances from the starting point as a function of time.

Let's assume the starting point is the origin (0 m).

For Igor:
Distance travelled by Igor (dI) = 8.0 m (since he starts 8.0 m behind Brian)
Speed of Igor (vI) = 7.0 m/s

For Brian:
Acceleration of Brian (aB) = 2.8 m/s^2
Initial velocity of Brian (uB) = 0 m/s (he starts from rest)
Distance travelled by Brian (dB) = distance travelled by Igor (dI) + distance ahead of Igor

Using the equations of motion:

For Igor:
dI = vI * tI

For Brian:
dB = uB * tB + (1/2) * aB * tB^2

Since we are comparing their distances at the same time, we can equate dI and dB:

vI * tI = uB * tB + (1/2) * aB * tB^2

Substituting the given values:
7.0 m/s * tI = 0 m/s * tB + (1/2) * 2.8 m/s^2 * tB^2

Simplifying the equation:
7.0 tI = 1.4 tB^2

We can rearrange the equation to compare the times:

tB^2 = (7.0 tI) / 1.4
tB^2 = 5.0 tI

Taking the square root of both sides:
tB = sqrt(5.0) * tI

Since tB > tI in this case (Brian accelerates away), Igor will not catch Brian.

Therefore, Igor will not catch Brian during the football game.