A satellite with a mass of 113 kg approaches a large planet at a speed vi,1 =10.3 km/s. The planet is moving at a speed vi,2 =14.6 km/s in the opposite direction. The satellite partially orbits the planet and then moves away from the planet in a direction opposite to its original direction (see the figure). If this interaction is assumed to approximate an elastic collision in one dimension, what is the speed of the satellite after the collision? This so-called slingshot effect is often used to accelerate space probes for journeys to distance parts of the solar system.

Question

A satellite with a mass of 113 kg approaches a large planet at a speed vi,1 =10.3 km/s. The planet is moving at a speed vi,2 =14.6 km/s in the opposite direction. The satellite partially orbits the planet and then moves away from the planet in a direction opposite to its original direction (see the figure). If this interaction is assumed to approximate an elastic collision in one dimension, what is the speed of the satellite after the collision? This so-called slingshot effect is often used to accelerate space probes for journeys to distance parts of the solar system.

Answer 1

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Answer 2

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Answer 3

Here it is almost April, and you still don't know anything about physics? How's that skipping class working out for you?

Answer 4

apply the law of conservation of momentum, and the law of conservation of energy.

You will have two equations, two unknowns (V1', V2').

I recommend the method of substitution.

Answer 5

To find the speed of the satellite after the collision, we can use the conservation of momentum and the concept of elastic collisions.

The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. In one dimension, this can be expressed as:

m1 * v1i1 + m2 * v1i2 = m1 * v1f1 + m2 * v1f2

Where:
m1 and m2 are the masses of the satellite and the planet respectively,
v1i1 and v1i2 are the initial velocities of the satellite and the planet,
v1f1 and v1f2 are the final velocities of the satellite and the planet.

In this case, the satellite moves towards the planet in the positive direction, while the planet moves in the opposite direction. After the collision, the satellite moves away from the planet in the negative direction (opposite to its original direction).

Given:
Mass of the satellite (m1) = 113 kg
Initial velocity of the satellite (v1i1) = 10.3 km/s
Initial velocity of the planet (v1i2) = -14.6 km/s

To solve the equation, we need to convert the velocities from km/s to m/s.

10.3 km/s * (1000 m/1 km) = 10,300 m/s
-14.6 km/s * (1000 m/1 km) = -14,600 m/s

Now, let's plug in the values into the equation:

113 kg * 10,300 m/s + m2 * (-14,600 m/s) = 113 kg * v1f1 + m2 * v1f2

Simplifying the equation, we get:

113 kg * 10,300 m/s + 14,600 m2/s = 113 kg * v1f1 - m2 * v1f2

Since the planet's mass (m2) is much larger than the satellite's mass (m1), we can assume that the planet's velocity does not change significantly. So we can set v1f2 approximately equal to v1i2:

113 kg * 10,300 m/s + 14,600 m2/s = 113 kg * v1f1 - m2 * v1i2

Now we can solve for v1f1:

v1f1 = (113 kg * 10,300 m/s + 14,600 m2/s + m2 * v1i2) / 113 kg

Finally, plug in the given values to calculate v1f1:

v1f1 = (113 kg * 10,300 m/s + 14,600 m2/s + m2 * (-14.6 km/s * (1000 m/1 km))) / 113 kg

Since we don't know the mass of the planet, we can't calculate the exact value of v1f1. However, using this formula and the given values, you can calculate the final velocity of the satellite after the collision.