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 72100 kg spacecraft by 63 cm/s, how long should it be fired?
a = F/m = 35/72100 = 4.85*10^-4 m/s^2.
t = 0.63/4.85*10^-4 = 1297.80 s.
To determine the time the rocket should be fired, we can use Newton's second law of motion, which relates the force applied on an object, the mass of the object, and the change in its velocity.
The equation is:
Force = Mass x Acceleration
Since the rocket has a thrust of 35 N, and we need to find the time it should be fired, we rearrange the equation to solve for time:
Time = (Mass x Change in velocity) / Thrust
First, we need to convert the change in velocity from centimeters per second (cm/s) to meters per second (m/s). Since 1 meter = 100 centimeters, the change in velocity is:
Change in velocity = 63 cm/s = 63/100 m/s = 0.63 m/s
Now we can plug the values into the equation:
Time = (72100 kg x 0.63 m/s) / 35 N
Calculating that:
Time = 136.53 s
Therefore, the rocket should be fired for approximately 136.53 seconds to change the velocity of the spacecraft.