Small rockets are used to make tiny adjustments in the speeds of satellites. One such rocket has a thrust of 35 N. If it is fired to change the velocity of a 71500 kg spacecraft by 63 cm/s, how long should it be fired?
To calculate the time the rocket should be fired, we can use Newton's second law of motion. The formula for this law is:
F = m * a
Where:
F is the force
m is the mass
a is the acceleration
In this case, the force exerted by the rocket is 35 N and the mass of the spacecraft is 71500 kg. We need to calculate the acceleration caused by the rocket.
First, we convert the change in velocity from centimeters per second to meters per second:
63 cm/s = 0.63 m/s
Now, we can rearrange the formula to solve for acceleration:
F = m * a
a = F / m
Substituting the values:
a = 35 N / 71500 kg
a ≈ 4.895 x 10^-4 m/s^2
Now, we can calculate the time the rocket should be fired using the formula:
Δv = a * t
Where:
Δv is the change in velocity
a is the acceleration
t is the time
Rearranging the formula, we get:
t = Δv / a
Substituting the values:
t = 0.63 m/s / (4.895 x 10^-4 m/s^2)
t ≈ 1288.45 s
Therefore, the rocket should be fired for approximately 1288.45 seconds (or approximately 21 minutes and 28 seconds) in order to change the velocity of the spacecraft by 63 cm/s.
To find the time the rocket should be fired, we can use Newton's second law of motion:
Force = mass × acceleration
In this case, the force is the thrust of the rocket (35 N) and the mass is the mass of the spacecraft (71,500 kg).
First, let's convert the change in velocity from centimeters per second to meters per second:
63 cm/s = 0.63 m/s
Now we can rearrange the equation to solve for acceleration:
acceleration = Force / mass
acceleration = 35 N / 71,500 kg
acceleration = 0.000489 m/s^2
Now we have the acceleration, and we can use the equation of motion to find the time it takes for the rocket to change the velocity:
change in velocity = acceleration × time
0.63 m/s = 0.000489 m/s^2 × time
Now we can solve for time:
time = 0.63 m/s / 0.000489 m/s^2
time ≈ 1288 seconds
Therefore, the rocket should be fired for approximately 1288 seconds to change the velocity of the spacecraft by 63 cm/s.