A football player weighing 75 kg running at 2 m/s toward west tackles a 70 kg player running 1.5 m/s in the opposite direction. What is the decrease in kinetic energy during the collision?

First use conservation of momentum to calculate the final velocity of both, V.

75*2 - 70*1.5 = 145 V
V = 0.31 m/s (west)

Now add up the initial and final kinetic energies.

KE1 = (1/2)*75*2^2 + (1/2)*70*(1.5)^2
= 150+ 78.75 = 228.75 J
KE2 = (1/2)*145*(0.31)^2 = 6.97 J

Subtract for the KE Loss. About 97% of the initial KE is lost.

A football player weighing 75 kg running at 2 m/s toward west tackles a 70 kg player running at 1.5 m/s in the opposite direction. What is the final velocity of the players if they both fall together

To find the decrease in kinetic energy during the collision, we need to first calculate the initial kinetic energy of each player and then the final kinetic energy after the collision.

The formula for kinetic energy is given by: KE = 0.5 * mass * velocity^2

Let's start by calculating the initial kinetic energy of the first player (player 1) running toward the west.

Mass of player 1 (m1) = 75 kg
Velocity of player 1 (v1) = 2 m/s

KE1 = 0.5 * m1 * v1^2
= 0.5 * 75 kg * (2 m/s)^2
= 0.5 * 75 kg * 4 m^2/s^2
= 150 m^2/s^2

Now, let's calculate the initial kinetic energy of the second player (player 2) running in the opposite direction.

Mass of player 2 (m2) = 70 kg
Velocity of player 2 (v2) = 1.5 m/s

KE2 = 0.5 * m2 * v2^2
= 0.5 * 70 kg * (1.5 m/s)^2
= 0.5 * 70 kg * 2.25 m^2/s^2
= 78.75 m^2/s^2

Now, we can calculate the total initial kinetic energy before the collision:

KE_initial = KE1 + KE2
= 150 m^2/s^2 + 78.75 m^2/s^2
= 228.75 m^2/s^2

After the collision, the players come to a stop, so their final velocities are both zero.

Since kinetic energy is given by 0.5 * mass * velocity^2, when velocity is zero, the kinetic energy is also zero.

The final kinetic energy after the collision is zero:

KE_final = 0 m^2/s^2

Therefore, the decrease in kinetic energy during the collision is given by:

ΔKE = KE_initial - KE_final
= 228.75 m^2/s^2 - 0 m^2/s^2
= 228.75 m^2/s^2

So, the decrease in kinetic energy during the collision is 228.75 m^2/s^2.

To find the decrease in kinetic energy during the collision, we need to calculate the initial and final kinetic energies of both players.

The formula for kinetic energy is: KE = 0.5 * mass * velocity^2

Let's calculate the initial kinetic energy for both players:

For the first player (75 kg, running at 2 m/s):
KE1 (initial) = 0.5 * 75 kg * (2 m/s)^2 = 0.5 * 75 * 4 = 150 Joules

For the second player (70 kg, running at 1.5 m/s):
KE2 (initial) = 0.5 * 70 kg * (1.5 m/s)^2 = 0.5 * 70 * 2.25 = 78.75 Joules

Now let's calculate the final kinetic energy after the collision. Since the players collide and come to rest, their final velocities are 0 m/s.

For the first player:
KE1 (final) = 0.5 * 75 kg * (0 m/s)^2 = 0 Joules

For the second player:
KE2 (final) = 0.5 * 70 kg * (0 m/s)^2 = 0 Joules

Finally, we can find the decrease in kinetic energy using the formula:
Decrease in kinetic energy = Initial kinetic energy - Final kinetic energy

For the first player:
Decrease in KE1 = KE1 (initial) - KE1 (final) = 150 Joules - 0 Joules = 150 Joules

For the second player:
Decrease in KE2 = KE2 (initial) - KE2 (final) = 78.75 Joules - 0 Joules = 78.75 Joules

Therefore, the total decrease in kinetic energy during the collision is the sum of the individual decreases:
Total decrease in kinetic energy = Decrease in KE1 + Decrease in KE2 = 150 Joules + 78.75 Joules = 228.75 Joules