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Chapter 5: Problem 49

What is the relative velocity of two spaceships if one fires a missile at the other at \(0.750 c\) and the other observes it to approach at \(0.950 c ?\)

Short Answer

Expert verified
The velocity of spaceship 2 relative to spaceship 1 is \(0.571c\).

Step by step solution

01

Understand the Given

First, identify the knowns. Here the speed of spaceship 1 (\(v_1\)) is \(0.750 c\). The relative speed of the missile as observed by spaceship 2 (\(v\)) is \(0.950 c\). We need to find the speed of spaceship 2 (\(v_2\)), the one that observes the missile.
02

Solve for the Velocity of Spaceship 2

Rearrange the relativistic addition of velocities equation to solve for \(v_2\). \(v_2\) can be given as: \(v_2 = \frac{v - v_1}{1- \frac{v * v_1}{c^2}}\).
03

Substitute the Known Values

Put the known values into the rearranged equation: \(v_2 = \frac{0.950c - 0.750c}{1 - \frac{0.950c * 0.750c}{c^2}}\).
04

Simplify the Equation that Helps to Find \(v_2\)

Divide the numerator and the denominator of the right-hand side by c. Then perform the multiplication and subtraction. Note that \(c^2/c^2 =1\). After performing these mathematical operations, simplify to find \(v_2\).

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Most popular questions from this chapter

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