A 94.0kg fullback moving south with a speed of 5.1m/s has a perfectly inelastic collision with a 90.0kg opponent running north at 3.0m/s.
A. Calculate the velocity of the players just after the tackle.
B. Calculate the decrease in total kinetic energy after the collision.
Anybody got an answer?
Can you us tell your answer first? Or, at least what you think?
A. I got -1.1m/s = Vf
B. I am having trouble with.
Can anybody help me?
To calculate the velocity of the players just after the tackle, we can use the principles of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Step 1: Find the initial momentum of each player.
The momentum of a player is calculated by multiplying its mass by its velocity. For the fullback:
Initial momentum of fullback = mass × velocity = 94.0 kg × 5.1 m/s = 479.4 kg·m/s
For the opponent:
Initial momentum of opponent = mass × velocity = 90.0 kg × (-3.0 m/s) (negative because the opponent is moving in the opposite direction) = -270.0 kg·m/s
Step 2: Apply the principle of conservation of momentum.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Total momentum before collision = Total momentum after collision
479.4 kg·m/s + (-270.0 kg·m/s) = Total momentum after collision
Step 3: Solve for the final velocity.
Since the collision is perfectly inelastic, the two players stick together after the tackle. Therefore, their final velocity will be the same.
Total momentum after collision = (mass of fullback + mass of opponent) × final velocity
Simplifying the equation:
479.4 kg·m/s + (-270.0 kg·m/s) = (94.0 kg + 90.0 kg) × final velocity
209.4 kg·m/s = 184.0 kg × final velocity
Dividing both sides by 184.0 kg:
final velocity = 209.4 kg·m/s / 184.0 kg
final velocity = 1.138 m/s
Therefore, the velocity of the players just after the tackle is approximately 1.138 m/s.
To calculate the decrease in total kinetic energy after the collision, we need to subtract the total kinetic energy after the collision from the total kinetic energy before the collision.
Step 1: Find the initial kinetic energy of each player.
The kinetic energy of a player is calculated by using the formula: KE = 0.5 × mass × velocity^2.
For the fullback:
Initial kinetic energy of fullback = 0.5 × 94.0 kg × (5.1 m/s)^2 = 1220.505 J
For the opponent:
Initial kinetic energy of opponent = 0.5 × 90.0 kg × (3.0 m/s)^2 = 405 J
Step 2: Find the final kinetic energy of the combined players.
Since the collision is perfectly inelastic, the two players stick together and move with a final velocity.
Total mass of the combined players = mass of fullback + mass of opponent = 94.0 kg + 90.0 kg = 184.0 kg
Final kinetic energy of the combined players = 0.5 × 184.0 kg × (1.138 m/s)^2 = 117.42 J
Step 3: Calculate the decrease in total kinetic energy.
Decrease in total kinetic energy = Initial kinetic energy - Final kinetic energy
= (1220.505 J + 405 J) - 117.42 J
= 1508 J - 117.42 J
= 1390.58 J
Therefore, the decrease in total kinetic energy after the collision is approximately 1390.58 J.