A model rocket engine has an average thrust of 5.26 n. it has an initial mass of 25.3 g, which includes fuel mass of 12.8 g. the duration of its burn is 1.90 s. (assume all the fuel is consumed.) (a) what is the average exhaust speed of the engine?

We are given that:

m0 = initial mass of rocket = 25.3 g

t = duration of the burn = 1.90 s

T = average thrust = 5.26 N

mFu = mass of fuel = 12.8 g

First we calculate the final mass after 1.90 s (mF):

mF = m0 - mFu = 25.3 g - 12.8 g = 12.5 g

Then we calculate for the mass rate of fuel consumption, φm:

φ m = 12.8 g / 1.90 s = 6.737 g / s

To calculate for the average exhaust speed (vF), we use the derived formula:

Δv = [T / φm] * ln (m0/mF)

Since the rocket started from rest, therefore Δv = vF

vF = [T / φm ] * ln (m0/mF)

vF = [5.26 N / 6.737 x 10^-3 kg/s] * ln (25.3 g / 12.5 g)

vF = 550.5 m/s