A 83.5-kg linebacker (\\\"X\\\") is running at 6.59 m/s directly toward the side

Question

A 83.5-kg linebacker ("X") is running at 6.59 m/s directly toward the sideline of a football field. He tackles a 86.5-kg running back ("O") moving at 9.27 m/s straight toward the goal line, perpendicular to the original direction of the linebacker. As a result of the collision both players momentarily leave the ground and go out-of-bounds at an angle relative to the sideline, as shown in the diagrams below. 1. What is the common speed of the players, immediately after their impact? 2. What is the angle, , of their motion, relative to the sideline?

Explanation / Answer

Conservation of momentum

For the line backer, M = 83.5 * 6.59 = 550.265
For the running back, M = 86.5 * 9.27 = 801.855
Since they have a common speed after the collision, they must be attached to each other after the collision. Let’s determine the total mass.

Total mass = 83.5 + 86.5 = 170 kg
Let use this mass to determine the components of their final velocity.
170 * v1 = 550.265
v1 =  3.237

170 * v2 = 801.855
v2 = 4.717
To determine the magnitude of their final velocity, use the following equation.

Speed = (v1^2 + v2^2)
v1^2 = 10.478
vf^2 = 22.25
Speed = [1.478 + 22.25]

Speed = 5.72 m/s.
To determine the direction, use the following equation.

Tan = v1/v2 = 3.237/4.717 = 0.6862
This is approximately 34.45.

OR

Tan = v2/v1 = 4.717/3.237 = 1.457
This is approximately 55.54

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