Question

Two asteroids head straight for Earth from the same direction. Their speeds relative to Earth are 0.78c for asteroid 1 and 0.58c for asteroid 2.

Find the speed of asteroid 1 relative to asteroid 2.
Express your answer using two significant figures

Answer 1

The speed of asteroid 1 relative to asteroid 2 is approximately 0.20c.

Step-by-step explanation:

The speed of asteroid 1 relative to asteroid 2 can be found by subtracting their velocities relative to Earth. Since both asteroids are heading straight for Earth from the same direction, their velocities can be added up to calculate their relative velocity to Earth.

Therefore, the speed of asteroid 1 relative to asteroid 2 is 0.78c - 0.58c = 0.20c, where 'c' is the speed of light in a vacuum (3 x 10^8 m/s).

Thus, the speed of asteroid 1 relative to asteroid 2 is approximately 0.20c.

Answer 2

To find the speed of asteroid 1 relative to asteroid 2, you can use the formula for relative velocity. Just plug in the given values and simplify the equation to find the final velocity.

Step-by-step explanation:

To find the speed of asteroid 1 relative to asteroid 2, we can use the formula for relative velocity. The formula for relative velocity is given by:

v' = (v1 - v2) / (1 - (v1 * v2 / c₂))

Where v' is the relative velocity, v1 is the velocity of asteroid 1 relative to Earth, v2 is the velocity of asteroid 2 relative to Earth, and c is the speed of light.

Plugging in the given values, we have:

v1 = 0.78c

v2 = 0.58c

c = speed of light = 3.00 x 10⁸ m/s

Substituting these values in the formula, we get:

v' = (0.78c - 0.58c) / (1 - (0.78c * 0.58c / (3.00 x 10⁸ m/s)²))

Simplifying this equation gives us the relative velocity of asteroid 1 with respect to asteroid 2.