In deep space, a 636 kg space probe, travels with an initial velocity of 19 m/s. Retro-rockets fire, producing a 212 N force in the opposite direction of the probe's initial velocity. How many seconds until the probe has a velocity of 22 m/s in the opposite direction of the initial velocity?
To find the time it takes for the probe to reach a velocity of 22 m/s in the opposite direction of its initial velocity, we can use Newton's second law of motion.
The formula is as follows:
Force = mass x acceleration
In this case, the force acting on the probe is the retro-rockets' force of 212 N, and the acceleration can be calculated by dividing the force by the mass of the probe.
Acceleration = Force / mass
Substituting the given values, we have:
Acceleration = 212 N / 636 kg
Dividing the force by the mass, we find that the acceleration is 0.3333 m/s².
Now, we can use a kinematic equation to find the time it takes for the velocity to change from 19 m/s to 22 m/s with a constant acceleration of -0.3333 m/s² (negative because it is acting in the opposite direction).
The equation we will use is:
vf = vi + at
Where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Substituting the known values, we get:
22 m/s = 19 m/s + (-0.3333 m/s²) * t
Simplifying the equation, we have:
3 m/s = (-0.3333 m/s²) * t
Now we can solve for t:
t = 3 m/s / (-0.3333 m/s²)
Calculating this, we find that the time it takes for the probe to reach a velocity of 22 m/s in the opposite direction is approximately 9 seconds.