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?
force*time= mass*velocity
massfuel*velocityfuel= masscar*velocitycar
massfuel(velocityfuel)=(masscar-massfuel)vcar
massfuel(velocityfuel+velocitycar)=masscar*vcar
but mass car=2000-mass fuel
Mf( )=2000Vcar-Mf*Vcar
Mf(Vf+2Vcar)=2000*Vcar
solve for Mf
check my work.
To find out how much fuel the rocket car exhausted during the 8 seconds, we need to apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system before an event is equal to the total momentum after the event, assuming no external forces are acting on the system.
In this case, we have a rocket car and its exhaust. Let's denote the mass of the rocket car as m_car and the mass of the fuel/exhaust as m_fuel. The initial velocity of the rocket car (before the exhaust) is 0 m/s, and the velocity of the exhaust is 1000 m/s due west. The final velocity of the rocket car after 8 seconds is 90 m/s due east.
According to the principle of conservation of momentum:
Total initial momentum = Total final momentum
The initial momentum of the system is 0, as the rocket car is at rest.
The final momentum of the system can be calculated as the sum of the momentum of the rocket car and the momentum of the exhaust:
Final momentum = (m_car × v_car) + (m_fuel × v_fuel)
Since the rocket car and the exhaust are moving in opposite directions, we use negative sign for the velocity of the exhaust.
Final momentum = m_car × v_car - m_fuel × v_fuel
Plugging in the given values:
m_car × 90 m/s - m_fuel × (-1000 m/s) = 0
Let's rearrange the equation to solve for m_fuel (mass of the fuel/exhaust):
m_fuel × 1000 m/s = m_car × 90 m/s
m_fuel = (m_car × 90 m/s) / 1000 m/s
Now, we can substitute the value of m_car, which is given as 2000 kg:
m_fuel = (2000 kg × 90 m/s) / 1000 m/s
m_fuel = 180000 kg * m/s / 1000 m/s
m_fuel = 180 kg
Therefore, the rocket car exhausted 180 kg of fuel during the 8 seconds.