A rocket has a mass of 0.8 kg and an engine that provides 100 N of force. A second rocket is being designed to use the same engine but accelerate at half the rate of the first rocket. What is the mass of the second rocket?
a
0.4 kg
b
1.6 kg
c
2.4 kg
d
0.8 kg
To find the mass of the second rocket, we can use Newton's second law of motion, which states that force equals mass times acceleration:
F = ma
In this case, we know the force provided by the engine (100 N) and the acceleration of the second rocket (half the acceleration of the first rocket).
For the first rocket:
F = ma
100 N = 0.8 kg * a
Solving for the acceleration, we find:
a = 100 N / 0.8 kg
a = 125 m/s^2
For the second rocket:
F = ma
100 N = m * (1/2 * 125 m/s^2)
Simplifying the equation, we have:
100 N = m * 62.5 m/s^2
Solving for m (the mass of the second rocket), we find:
m = 100 N / 62.5 m/s^2
m = 1.6 kg
Therefore, the mass of the second rocket is 1.6 kg.
The correct option is b) 1.6 kg.