Randy, a 105kg running back, is running to the west with a football at a speed of 6.75(m)/(s). Larry, a 155kg linebacker is running at 7.25(m)/(s) to the north. They collide as Larry tackles Randy. What is the resulting velocity of the two players after the collision?

To find the resulting velocity of Randy and Larry after the collision, we use the conservation of momentum. We calculate momentum for each player, sum it to find total momentum, and then use the Pythagorean theorem to determine the combined velocity's magnitude and direction after the collision.

The resulting velocity after a collision, which is an application of the conservation of momentum in Physics. To solve this, we must first recognize that momentum is a vector quantity, meaning it has both magnitude and direction. Since the collision is two-dimensional, we compute the momentum in each direction separately and then combine them to find the final velocity vector.

Let's assume Randy and Larry stick together after the collision. The total momentum before the collision is the sum of Randy’s and Larry’s individual momenta. Using the conservation of momentum, the combined momentum of Randy and Larry should be equal to their total momentum before the collision.

Step-by-Step Calculation:

Calculate Randy's momentum: (105kg) * (6.75m/s) = 708.75kg*m/s to the west.
Calculate Larry's momentum: (155kg) * (7.25m/s) = 1123.75kg*m/s to the north.
Since momentum is conserved, the total momentum in each direction stays the same after the collision.
Next, we find the magnitude of the resulting velocity using the Pythagorean theorem because we have a right-angle collision.
Finally, to find the direction of the resulting velocity, we need to calculate the angle of the velocity vector using trigonometry.