A rocket whish is in deep space and initially at rest relative to an inertial reference frame, has a mass of 2.55 X 10^5 kg of which 1.81 X10^5 kg is fuel. The rocket engine is then fired for 250 s during which feul is consumed at the rate of 480 kg/s. The speed of the exhaust products relative toe the rock is 3.27 km/s. a) what is the rocket’s thrust? B) After the 250s firing what is the mass c) the speed of the rocket after the 250s firing?
a) I would multiply 1.81x10^5*480
b) Would I used the answer from a) and divide by acceleration?
c)i am not sure what to do for this part
Thrust=mv/t= m/t *v You are given the fuel burn rate (m/t) and v.
massleft= intial mass - fuelburnrate*time
Speed of rocket= thrust*timeburn/avgmassrocket
where average mass of rocket= starting mass -fuelburned/2
a) To find the rocket's thrust, we can use the formula thrust = (mass flow rate) * (exhaust velocity). We are given the mass flow rate (480 kg/s) and the exhaust velocity (3.27 km/s). We need to convert the exhaust velocity to the SI unit, meters per second.
3.27 km/s = 3270 m/s
Thrust = (480 kg/s) * (3270 m/s) = 1,569,600 N
b) To find the mass of the rocket after the 250 s firing, we can subtract the mass of fuel consumed from the initial mass. We know the initial mass of the rocket (2.55 x 10^5 kg), the initial mass of fuel (1.81 x 10^5 kg), and the fuel consumption rate (480 kg/s). We can calculate the mass of fuel consumed during the 250 s firing:
Fuel consumed = (480 kg/s) * (250 s) = 1.20 x 10^5 kg
The mass of the rocket after the firing is the initial mass minus the mass of fuel consumed:
Remaining mass = (2.55 x 10^5 kg) - (1.20 x 10^5 kg) = 1.35 x 10^5 kg
c) As per the third equation in the initial answer, we can find the speed of the rocket after the 250 s firing.
Speed of the rocket = (Thrust * Timeburn) / Avgmassrocket
The initial mass of the rocket is 2.55 x 10^5 kg, and the mass of fuel consumed during the firing is 1.20 x 10^5 kg. So, the average mass of the rocket during the firing is:
Avgmassrocket = (Initial mass + Remaining mass) / 2 = (2.55 x 10^5 kg + 1.35 x 10^5 kg) / 2 = 1.95 x 10^5 kg
Now, we can calculate the speed of the rocket after the firing:
Speed of rocket = (1,569,600 N * 250 s) / (1.95 x 10^5 kg) = 2010 m/s
a) To calculate the rocket's thrust, you would multiply the fuel burn rate by the speed of the exhaust products. So, the formula would be:
Thrust = (fuel burn rate) * (speed of exhaust products)
In this case, the fuel burn rate is given as 480 kg/s and the speed of the exhaust products is given as 3.27 km/s. So, you would calculate:
Thrust = 480 kg/s * 3.27 km/s
Make sure to convert the speed to the same units as the fuel burn rate (in this case, kg/s). Since 1 km = 1000 m, you can convert km/s to m/s by multiplying by 1000.
b) To find the mass of the rocket after the 250s firing, you need to subtract the fuel consumed during that time from the initial mass of the rocket. The fuel burn rate is given as 480 kg/s, and the firing time is 250 s. So, the formula would be:
Mass after firing = Initial mass - (fuel burn rate * firing time)
Given that the initial mass is 2.55 x 10^5 kg, you can substitute the values into the formula:
Mass after firing = 2.55 x 10^5 kg - (480 kg/s * 250 s)
c) To find the speed of the rocket after the 250s firing, you can use the concept of conservation of momentum. The formula is:
Speed of rocket = Thrust * Time of burn / Average mass of rocket
From part b), you have the mass of the rocket after the firing. To find the average mass of the rocket, subtract the amount of fuel burned during the firing from the initial mass and divide by 2:
Average mass of rocket = (Initial mass - Fuel burned) / 2
Now, you can substitute the values into the formula:
Speed of rocket = Thrust * 250 s / Average mass of rocket
Remember to use the value of thrust calculated in part a) and the average mass of the rocket from part b).
a) To calculate the rocket's thrust, you would multiply the fuel burn rate by the velocity of the exhaust products relative to the rocket.
Thrust = (1.81 × 10^5 kg) * (480 kg/s) * (3.27 km/s)
b) After the 250s firing, the mass of the rocket can be calculated as the difference between the initial mass and the total amount of fuel burned during the 250s.
Mass = Initial mass - (fuel burn rate * time)
c) To calculate the speed of the rocket after the 250s firing, you can use the equation:
Speed of rocket = Thrust * time of burn / average mass of rocket
Where the average mass of the rocket is calculated as:
Average mass of rocket = (initial mass - fuel burned) / 2