A 76.7-kg linebacker (\"X\") is running at 6.71 m/s directly toward the sideline

Question

A 76.7-kg linebacker ("X") is running at 6.71 m/s directly toward the sideline of a football field. He tackles a 91.7-kg running back ("O") moving at 8.83 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 theta relative to the sideline, as shown in the diagrams below. What is the common speed of the players, immediately after their impact? What is the angle. theta, of their motion, relative to the sideline?

Explanation / Answer

Here,

right as positive x direction

upwards as positive y direction

let the final speed is v

and the angle is phi

Using conservation of momentum

Total initial momentum = total final momentum

76.7 * 6.71 j + 91.7 * 8.83 i = (76.7 + 91.7) * v

solving for v

v = 4.81 i + 3.06 j

magnitude of common velocity = sqrt(4.81^2 + 3.06^2)

magnitude of common velocity = 5.7 m/s

the magnitude of common velocity is 5.7 m/s
----------------------------

phi = arctan(3.06/4.81)

phi = 32.45 degree

the angle phi realtive to motion is 32.45 degree

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