001 (part 1 of 2) 10.0 points
An 86 kg fullback moving east with a speed
of 5.5 m/s is tackled by a 97 kg opponent
running west at 3.6 m/s, and the collision is
perfectly inelastic.
a) What is the velocity of the players immediately after the tackle?
Answer in units of m/s.
002 (part 2 of 2) 10.0 points
b) What is the decrease in kinetic energy
during the collision?
Answer in units of J.
To answer part (a) of the question, we need to apply the principle of conservation of momentum. In an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. So, we can calculate the initial momentum and final momentum to find the velocity of the players immediately after the tackle.
Let's calculate the initial momentum (before the collision) and final momentum (after the collision):
Initial momentum of the fullback (moving east) = mass of the fullback * velocity of the fullback
Final momentum of the players (after the tackle) = total mass of the players * final velocity
Since momentum is conserved, we can write:
Initial momentum = Final momentum
(mass of the fullback * velocity of the fullback) = (total mass of the players * final velocity)
Using the given data:
Mass of the fullback (m1) = 86 kg
Velocity of the fullback (v1) = 5.5 m/s
Mass of the opponent (m2) = 97 kg
Velocity of the opponent (v2) = -3.6 m/s (opposite direction)
Total mass of the players (m1 + m2) = 86 kg + 97 kg
Now, we can calculate the final velocity of the players:
Initial momentum = Final momentum
(m1 * v1) = ((m1 + m2) * final velocity)
(86 kg * 5.5 m/s) = ((86 kg + 97 kg) * final velocity)
Solve the equation to find the final velocity of the players.
To answer part (b) of the question, we need to calculate the decrease in kinetic energy during the collision. The change in kinetic energy can be calculated using the following formula:
Change in kinetic energy = Initial kinetic energy - Final kinetic energy
The initial kinetic energy can be calculated using:
Initial kinetic energy = (1/2) * (mass of the fullback * velocity of the fullback^2) + (1/2) * (mass of the opponent * velocity of the opponent^2)
The final kinetic energy can be calculated using:
Final kinetic energy = (1/2) * (total mass of the players * final velocity^2)
Plug in the values and calculate the decrease in kinetic energy.
Remember to convert the final velocity to the proper sign convention (positive or negative) based on the directions mentioned in the problem.