Miguel, the 72.0 kg bullfighter, runs toward an angry bull at a speed of 4.00 m/s. The 550 kg bull charges toward Miguel at 12.0 m/s amd Miguel must jump on the bull's back at the last minute to avoid being run over. What is the new velocity of Miguel and the bull as they move across the arena?
M1V1+M2V2=(M1+M2)V
V1+V2=V
To find the new velocity of Miguel and the bull as they move across the arena, we need to use the principles of conservation of momentum.
The momentum before the jump can be calculated by multiplying the mass of an object by its velocity. Therefore, the initial momentum of Miguel can be calculated as follows:
Initial momentum of Miguel = mass of Miguel × velocity of Miguel
= 72.0 kg × 4.00 m/s
= 288 kg·m/s.
Similarly, the initial momentum of the bull can be calculated as follows:
Initial momentum of the bull = mass of the bull × velocity of the bull
= 550 kg × 12.0 m/s
= 6600 kg·m/s.
According to the law of conservation of momentum, the total momentum before and after the jump should be equal. Therefore, the total momentum after the jump will also be 288 kg·m/s + 6600 kg·m/s = 6888 kg·m/s.
Let's assume the new velocity of both Miguel and the bull after the jump is V. We can use the equation:
Total momentum after the jump = (mass of Miguel + mass of the bull) × V.
Therefore,
6888 kg·m/s = (72.0 kg + 550 kg) × V.
To find V, we can solve the equation by dividing both sides by (72.0 kg + 550 kg):
V = 6888 kg·m/s / (72.0 kg + 550 kg).
V ≈ 11.05 m/s (rounded to two decimal places).
Therefore, the new velocity of Miguel and the bull as they move across the arena is approximately 11.05 m/s.
M1V1+M2V2=(M1+M2)V
solve for V