A rocket of 30000kg mass acquires a speed of 2000k after takeoff. The power expended during this time is in 1minute?
the acceleration of the rocket is (2000km/s)/(60s) = 1/3 * 10^5 m/s^2
The distance traveled by the rocket is 1/2 * 1/3 * 10^5 * (60s)^2 = 6 * 10^7 m
The work done lifting the rocket to that height is 3000*9.8 * 6*10^7 = 1.764*10^12 J
The power was thus 1.764*10^12/60 = 2.94*10^10 W
oops. was 2000k supposed to be km/hr?
I made it 2000km/s !!
Probably not what was wanted...
I'm sure you can make the adjustment.
To calculate the power expended during the takeoff of a rocket, you need to use the equation:
Power (P) = Work (W) / (time (t))
To find the work done, you need to calculate the change in kinetic energy of the rocket, which can be determined using the formula:
ΔKE = 1/2 * m * (v^2 - u^2)
where:
ΔKE = change in kinetic energy
m = mass of the rocket (30,000 kg)
v = final velocity of the rocket (2,000 m/s)
u = initial velocity of the rocket (assumed to be 0 m/s, as it starts from rest during the takeoff)
Substituting these values into the formula, we have:
ΔKE = 1/2 * 30,000 * (2,000^2 - 0^2)
= 1/2 * 30,000 * 4,000,000
Now, calculate the work done by multiplying the change in kinetic energy with the distance traveled:
W = ΔKE * d
Since the distance is not given in the question, we cannot proceed with calculating the power. The power expended during the takeoff cannot be determined without knowing the distance traveled by the rocket.