Question

At a particular instant the magnitude of the momentum of a planet is 2.05 ✕ 10²⁹ kg · m/s, and the force exerted on it by the star it is orbiting is 9.0 ✕ 10²² N. The angle between the planet's momentum and the gravitational force exerted by the star is 127°. What will the magnitude of the planet's momentum be after 6 h?

Answer 1

To find the planet's new momentum after 6 hours, calculate the impulse using the force's component in the direction of the momentum's change and add this to the original momentum.

Step-by-step explanation:

To determine the magnitude of the planet's momentum after 6 hours, given an initial momentum of 2.05 × 10²¹ kg · m/s and a gravitational force of 9.0 × 10²² N exerted at an angle of 127°, we need to calculate the change in momentum (impulse) and then add it to the initial momentum. Since momentum is a vector quantity, we must consider the direction of the force related to the direction of the momentum.

To find the impulse, we need to calculate the component of the force in the direction of the momentum's change, which can be done using trigonometry (Force component = F × cos(180° - 127°)). Then, we use the formula Impulse = Force component × Time to get the change in momentum over 6 hours (21,600 seconds). Finally, the magnitude of the new momentum is the vector sum of the initial momentum and the impulse.