Running at 2.0 m/s a 45.0 kg person collides with a 90.0 kg person who is traveling at 7.0 m/s in the other direction. Upon collision, the 90 kg person continues to travel forward at 1.0 m/s. How fast is the 45 kg person knocked backwards?

Given: m/s.

M 1 = 45 kg, V1 = 2 m/s.
M2 = 90 kg, V2 = -7 m/s.
V3 = Velocity of M1 after collision.
V4 = -1 m/s = Velocity of M2 after collision.

Momentum before = Momentum after
M1*V1 + M2*V2 = M1*V3 + M2*V4.
45*2 + 90*(-7) = 45V3 + 90*(-1),
90 - 630 = 45V3 - 90,
-450 = 45V3,
V3 = -10 m/s.

To solve this problem, we can use the principle of conservation of momentum. The momentum of an object can be calculated by multiplying its mass by its velocity. According to the law of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.

Let's calculate the initial momentum before the collision:

Person 1 (45 kg) initial momentum:
Momentum = mass * velocity = 45 kg * 2.0 m/s = 90 kg·m/s

Person 2 (90 kg) initial momentum:
Momentum = mass * velocity = 90 kg * (-7.0 m/s) = -630 kg·m/s

Since the two people are moving in opposite directions, one of the velocities should have a negative sign.

Now, let's calculate the final momentum after the collision:

Person 1 (45 kg) final momentum:
Since the 90 kg person continues to travel forward at 1.0 m/s, the 45 kg person would move backward.
Momentum = mass * velocity = 45 kg * (-v) m/s = -45v kg·m/s, where v is the velocity of the 45 kg person after the collision.

Person 2 (90 kg) final momentum:
Momentum = mass * velocity = 90 kg * 1.0 m/s = 90 kg·m/s

According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision:

Initial momentum = Final momentum
90 kg·m/s + (-630 kg·m/s) = -45v kg·m/s + 90 kg·m/s

-540 kg·m/s = -45v kg·m/s + 90 kg·m/s

Now, solve for v (the velocity of the 45 kg person after the collision):

-540 kg·m/s - 90 kg·m/s = -45v kg·m/s

-630 kg·m/s = -45v kg·m/s

Divide both sides by -45 kg·m/s:

14 m/s = v

Therefore, the 45 kg person is knocked backward at a speed of 14.0 m/s.