Question

A 5.9 x 104-kg space probe is traveling at a speed of 14000 m/s through deep space. Retrorockets are fired along the line of motion to

reduce the probe's speed. The retrorockets generate a force of 1.4 x 104 N over a distance of 3700 km. What is the final speed of the
probe?

Answer 1

To calculate the final speed of the space probe, we can use the principle of conservation of momentum. The final speed is approximately 136.8 m/s.

Step-by-step explanation:

To calculate the final speed of the space probe, we can use the principle of conservation of momentum. The initial momentum of the probe is given by its mass multiplied by its initial velocity:

Initial momentum = mass x initial velocity

The final momentum of the probe is given by its final mass (mass of the probe minus the mass of the expelled fuel) multiplied by its final velocity:

Final momentum = (mass - mass of fuel) x final velocity

Since the gravitational force is negligible, we can assume that the initial and final momentum are equal:

mass x initial velocity = (mass - mass of fuel) x final velocity

Plugging in the given values:

(5.9 x 10^4) kg x (14000) m/s = (5.9 x 10^4 - 3.7 x 10^6) kg x final velocity

Solving for the final velocity, we find that the probe's final speed is approximately 136.8 m/s.