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?
According to Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration.
For the first rocket:
F = 100 N
m = 0.8 kg
a= F / m = 100 N / 0.8 kg = 125 m/s^2
For the second rocket:
F = 100 N
a= 1/2 * 125 m/s^2 = 62.5 m/s^2
Let's assume the mass of the second rocket is m2.
F = 100 N
m = m2
a = 62.5 m/s^2
Using the equation F = ma, we can solve for m2:
100 N = m2 * 62.5 m/s^2
Divide both sides by 62.5 m/s^2:
100 N / 62.5 m/s^2 = m2
m2 = 1.6 kg
So, the mass of the second rocket is 1.6 kg.