Your teacher bumps into you in the hallway and knocks you down. After he apologizes, he asks you to figure out how fast he was going. By some magical coincidence, you just happened to be wearing a gauge that measured your mass to be 75 kilograms and your speed to be 25 miles per hour as you were falling. If your teacher has a mass of 85 kilograms, how fast was he going?

To determine how fast your teacher was going, we can use the concept of conservation of momentum. In a collision between two objects, the total momentum before the collision is equal to the total momentum after the collision.

In this scenario, we can assume that your momentum before the collision is equal to your mass multiplied by your speed. So, your momentum can be calculated as:

Your momentum = Your mass * Your speed

Your momentum = 75 kg * 25 miles per hour

Before we go any further, we need to convert your speed from miles per hour to meters per second to match the SI units (International System of Units) used in physics equations.

To convert miles per hour to meters per second, we can use the conversion factor of 1 mile = 1.60934 kilometers and 1 kilometer = 1000 meters. So:

Your speed in meters per second = Your speed in miles per hour * (1 mile/1.60934 kilometers) * (1000 meters/1 kilometer) * (1 hour/3600 seconds)

Using this conversion, we can find your speed in meters per second.

Your speed in meters per second ≈ 25 * (1 mile/1.60934 kilometers) * (1000 meters/1 kilometer) * (1 hour/3600 seconds)

Now that we know your speed in meters per second, we can calculate your momentum.

Your momentum = 75 kg * (Your speed in meters per second)

Next, we can use the conservation of momentum concept to find your teacher's speed. Since the total momentum before the collision is equal to the total momentum after the collision, we can write the equation as:

Your momentum + Your teacher's momentum before the collision = Your momentum + Your teacher's momentum after the collision

Considering that the only unknown in this equation is your teacher's momentum after the collision, we can solve for it.

Your momentum + Your teacher's momentum before the collision = Your momentum + Your teacher's momentum after the collision

75 kg * (Your speed in meters per second) + 85 kg * Your teacher's speed = 75 kg * (Your speed in meters per second) + 85 kg * Your teacher's final speed

Since your teacher's speed before the collision is what we need to determine, we can substitute the known values and solve for it.

75 kg * (Your speed in meters per second) + 85 kg * Your teacher's speed = 75 kg * (Your speed in meters per second) + 85 kg * Your teacher's final speed

Simplifying the equation, we find:

85 kg * Your teacher's speed = 85 kg * Your teacher's final speed

Dividing both sides of the equation by 85 kg, we get:

Your teacher's speed = Your teacher's final speed

Therefore, the speed at which your teacher was going is equal to his final speed. Based on the conservation of momentum principle, your teacher's initial speed is the same as his final speed.

So, based on the information given, your teacher's speed, which caused the collision, is equal to your speed of 25 miles per hour (after conversion to meters per second).