The mass of a rocket car plus fuel is 2,000kg. The rocket car starts from rest. The engine expels fuel(in the form of exhaust) over a period of 8 seconds. The exhaust has a velocity of 1,000m/s due west, and the velocity of the rocket car after 8 seconds is 90m/s due east. How much fuel did the rocket car exhaust during the 8 seconds?
To find out how much fuel the rocket car exhausted during the 8 seconds, we can use the principle of conservation of momentum.
First, let's calculate the initial momentum of the system (rocket car + fuel) before the exhaust occurs:
Initial momentum = mass × velocity
Initial momentum = (mass of rocket car + mass of fuel) × velocity of rocket car
Given that the mass of the rocket car plus fuel is 2,000 kg, and the rocket car starts from rest (initial velocity = 0 m/s), we have:
Initial momentum = 2,000 kg × 0 m/s
Initial momentum = 0 kg·m/s
Next, let's calculate the final momentum of the system after the exhaust has occurred:
Final momentum = (mass of rocket car) × (velocity of rocket car) + (mass of fuel) × (velocity of exhaust)
Given that the velocity of the rocket car after 8 seconds is 90 m/s and the velocity of the exhaust is 1,000 m/s, we can represent the final momentum as:
Final momentum = (mass of rocket car) × 90 m/s + (mass of fuel) × (-1,000 m/s)
Note that the velocity of the exhaust is negative (due west), causing the opposite direction of the rocket car's velocity.
Since the initial momentum and the final momentum should be equal according to the conservation of momentum principle, we can equate the two:
0 kg·m/s = (mass of rocket car) × 90 m/s + (mass of fuel) × (-1,000 m/s)
Now, we need to solve this equation to find the mass of the fuel exhausted during the 8 seconds.
However, we're missing a crucial piece of information - the mass of the rocket car. Without knowing this, we cannot determine the mass of the fuel exhausted. Could you provide the mass of the rocket car?