In a football game, a tackle running at a constant speed of 5 m/s tackles a stationary receiver. The two fly off horizontally at 4 m/s, before they hit the ground and begin to slow down. If the mass of the tackle is 105 kg,
a.) What is the mass of the receiver?
1Your answer is incorrect.
b.) Calculate the kinetic energy of the tackle-receiver system before and after the collision.
I tried the formula for question a.) to set the initial and final momentum to be equal, but I keep getting the mass wrong...help?
To solve this problem, we need to use the principles of conservation of momentum and conservation of kinetic energy. Let's break it down step by step:
a.) To find the mass of the receiver, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the tackle is running at a speed of 5 m/s and has a mass of 105 kg. Since the receiver is stationary, their initial momentum is zero.
After the collision, both the tackle and the receiver fly off horizontally at a speed of 4 m/s. We know the mass of the tackle is 105 kg.
Let's denote the mass of the receiver as 'm'. The total momentum after the collision is given by the equation:
(105 kg) * (5 m/s) + m * (0 m/s) = (105 kg) * (4 m/s) + m * (4 m/s)
Simplifying this equation, we get:
525 kg⋅m/s = 420 kg⋅m/s + 4m kg⋅m/s
Subtracting 420 kg⋅m/s from both sides, we find:
105 kg⋅m/s = 4m kg⋅m/s
Now we can cancel out the kg⋅m/s units:
105 = 4m
Dividing both sides by 4, we get:
m = 26.25 kg
Therefore, the mass of the receiver is approximately 26.25 kg.
b.) To calculate the kinetic energy of the tackle-receiver system before and after the collision, we need to consider the kinetic energy formulas:
Kinetic energy = 0.5 * mass * (velocity)^2
Before the collision:
The kinetic energy of the tackle (105 kg) can be calculated using the formula:
Kinetic energy = 0.5 * 105 kg * (5 m/s)^2
Simplifying this expression, we find:
Kinetic energy before = 0.5 * 105 kg * 25 m^2/s^2
After the collision:
The total kinetic energy of the tackle-receiver system is given by the equation:
Kinetic energy = 0.5 * (105 kg + 26.25 kg) * (4 m/s)^2
Simplifying this expression, we get:
Kinetic energy after = 0.5 * 131.25 kg * 16 m^2/s^2
Now you can calculate both the kinetic energy before and after the collision using the formulas.