A 92.3 kg football quarterback attempts to carry the ball to the goal line, running at 7.52 m/s [W]. He is tackled by an opposing 124 kg defensive lineman charging at 4.74 m/s [N]. Based on the information, what is the combined velocity of the two players immediately after impact?

Using the principle of conservation of momentum, the combined velocity of the two football players after impact can be calculated. In this case, the speed after impact would be approximately 4.2 m/s.

Explanation:

To calculate the combined velocity of the two football players after impact, we need to apply the principle of conservation of momentum. In an isolated system, the total momentum before the collision is equal to the total momentum after the collision. The lineman's momentum is mass x velocity which is 124kg * 4.74 m/s = 588.56 kg*m/s. The quarterback's momentum is similarly calculated as 92.3kg * 7.52 m/s = 693.776 kg*m/s.

Given they are tackling each other from perpendicular directions [W] and [N], we treat this as a two-dimensional problem which involves computing the result of their momentum vectors. But since we are asked only for the speed, we calculate the total momentum magnitude with the Pythagorean theorem: √[(588.56 kg*m/s)² + (693.776 kg*m/s)²] = 907.77 kg*m/s. This total momentum is shared by their combined mass (124 kg + 92.3 kg = 216.3 kg) after the collision.

Therefore, their combined velocity or speed after the collision is total momentum / total mass which gives 907.77 kg*m/s / 216.3kg = approximately 4.2 m/s.

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