Part A

This is a problem of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

The momentum of the linebacker before the collision is his mass times his velocity, or (120 kg)(8.5 m/s) = 1020 kg*m/s north.

The momentum of the halfback before the collision is his mass times his velocity, or (75 kg)(7.2 m/s) = 540 kg*m/s east.

After the collision, the two players move together, so their combined mass is 120 kg + 75 kg = 195 kg.

The total momentum after the collision is the vector sum of the two momenta before the collision. This is a right triangle, so we can use the Pythagorean theorem to find the magnitude of the total momentum:

P_total = sqrt((1020 kg*m/s)^2 + (540 kg*m/s)^2) = 1152.38 kg*m/s

The velocity of the two players moving together is their total momentum divided by their total mass, or (1152.38 kg*m/s) / (195 kg) = 5.91 m/s.

Part B

The direction of the velocity can be found using trigonometry. The angle θ can be found using the tangent function:

tan(θ) = (momentum of halfback) / (momentum of linebacker)
tan(θ) = (540 kg*m/s) / (1020 kg*m/s)

θ = arctan((540 kg*m/s) / (1020 kg*m/s)) = 27.47 degrees

However, this angle is measured from the north, towards the east. The convention is to measure the angle from the east, towards the north, so the actual angle is 90 degrees - 27.47 degrees = 62.53 degrees.

So, the two players move together at a speed of 5.91 m/s, in a direction 62.53 degrees north of east.

Question

Part A

This is a problem of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

The momentum of the linebacker before the collision is his mass times his velocity, or (120 kg)(8.5 m/s) = 1020 kg*m/s north.

The momentum of the halfback before the collision is his mass times his velocity, or (75 kg)(7.2 m/s) = 540 kg*m/s east.

After the collision, the two players move together, so their combined mass is 120 kg + 75 kg = 195 kg.

The total momentum after the collision is the vector sum of the two momenta before the collision. This is a right triangle, so we can use the Pythagorean theorem to find the magnitude of the total momentum:

P_total = sqrt((1020 kg*m/s)^2 + (540 kg*m/s)^2) = 1152.38 kg*m/s

The velocity of the two players moving together is their total momentum divided by their total mass, or (1152.38 kg*m/s) / (195 kg) = 5.91 m/s.

Part B

The direction of the velocity can be found using trigonometry. The angle θ can be found using the tangent function:

tan(θ) = (momentum of halfback) / (momentum of linebacker)
tan(θ) = (540 kg*m/s) / (1020 kg*m/s)

θ = arctan((540 kg*m/s) / (1020 kg*m/s)) = 27.47 degrees

However, this angle is measured from the north, towards the east. The convention is to measure the angle from the east, towards the north, so the actual angle is 90 degrees - 27.47 degrees = 62.53 degrees.

So, the two players move together at a speed of 5.91 m/s, in a direction 62.53 degrees north of east.

Knowee AI · Accepted Answer