Answer: The answer for A is - v = 786.93 m/s
The answer for B is - v = 122.40 m/s
Explanation:
a) To find the average exhaust speed (v) of the engine we can use the following equation:
F = vΔm
Where:
F: is the thrust by the engine = 5.26 N
Δm: is the mass of the fuel = 12.7 g
Δt: is the time of the burning of fuel = 1.90 s
v = F×ΔT/ΔT
b) To calculate the final velocity of the rocket we need to find the acceleration.
The acceleration (a) can be calculated as follows:
a = F/M
In the above equation, m is an average between the mass of the engine plus the rocket case mass and the mass of the engine plus the rocket case minus the fuel mass:
m = (m_{engine} + m_{rocket}) + (m_{engine} + m_{rocket} - m_{fuel})}{2} = {2*m_{engine} + 2*m_{rocket} - m_{fuel}}{2} = 2*25.0 g + 2*63.0 g - 12.7 g}{2} = 81.65 g
Now, the acceleration is:
a = 5.26 N/81.65-t 10^³kg} = 64.42 m*s^²
Finally, the final velocity of the rocket can be calculated using the following kinematic equation:
v= v_{0} + at = 0 + 64.42 m*s^{-2}*1.90 s = 122.40 m/s
