A stationary 165 kg football player is tackled by a 178 kg player running at 8 m/s.
How fast are they moving after the collision?
What is the impulse imparted on the stationary player?
What is the impulse imparted on the moving player?
To determine the speed at which the players are moving after the collision and the impulses imparted on each player, we can use the principle of conservation of momentum and the equations for impulse.
1. Speed after the collision:
The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
(m1 * v1) + (m2 * v2) = (m1 * v1') + (m2 * v2')
Where:
- m1 and m2 are the masses of the two players
- v1 and v2 are the initial velocities of the two players
- v1' and v2' are the final velocities of the two players
In this case, the first player is stationary, so v1 = 0 m/s. The second player is running at 8 m/s, so v2 = 8 m/s. Let's assume the final velocities are v1' and v2', respectively.
Plugging in the given values, we have:
(165 kg * 0 m/s) + (178 kg * 8 m/s) = (165 kg * v1') + (178 kg * v2')
Simplifying the equation, we get:
1424 kg m/s = 165 kg * v1' + 1424 kg m/s
To find the final velocity of the first player (v1'), we can subtract 1424 kg m/s from both sides and divide by the mass of the first player (165 kg):
v1' = (1424 kg m/s - 1424 kg m/s) / 165 kg
v1' = 0 m/s
Substituting the value of v1' back into the equation, we can solve for v2':
(165 kg * 0 m/s) + (178 kg * 8 m/s) = (165 kg * 0 m/s) + (178 kg * v2')
(1424 kg m/s) = (178 kg * v2')
Dividing both sides by the mass of the second player (178 kg), we get:
v2' = (1424 kg m/s) / 178 kg
v2' ≈ 8 m/s
Therefore, after the collision, both players are moving at approximately 8 m/s.
2. Impulse imparted on the stationary player:
The impulse experienced by an object can be calculated using the equation:
Impulse = change in momentum
For the stationary player, the initial momentum is zero (m1 * v1 = 0), and the final momentum is (m1 * v1'). Therefore, the impulse experienced by the stationary player is:
Impulse1 = m1 * (v1' - v1)
Impulse1 = 165 kg * (0 m/s - 0 m/s)
Impulse1 = 0 kg m/s
Therefore, the impulse imparted on the stationary player is 0 kg m/s.
3. Impulse imparted on the moving player:
Using the same equation, the impulse experienced by the moving player is:
Impulse2 = m2 * (v2' - v2)
Impulse2 = 178 kg * (8 m/s - 8 m/s)
Impulse2 = 0 kg m/s
Therefore, the impulse imparted on the moving player is also 0 kg m/s.