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 solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
For the first rocket, we know that the mass is 0.8 kg and the force is 100 N. We can rearrange the formula as follows:
force = mass * acceleration
100 N = 0.8 kg * acceleration
Solving for acceleration, we get:
acceleration = 100 N / 0.8 kg
acceleration = 125 m/s²
Now, for the second rocket, we know that it accelerates at half the rate of the first rocket. So the acceleration of the second rocket is:
acceleration = 125 m/s² / 2
acceleration = 62.5 m/s²
Finally, we can rearrange Newton's second law to solve for mass:
mass = force / acceleration
mass = 100 N / 62.5 m/s²
mass = 1.6 kg
Therefore, the mass of the second rocket is 1.6 kg.
Answer: b. 1.6 kg