Bob and Bob Jr. stand at open doorways at opposite ends of an airplane hangar 25 m long. Anna owns a spaceship, 40 m long as it sits on the runway. Anna takes off in her spaceship, then swoops through the hangar at constant velocity. At precisely time zero on both Bob's clock and Anna's, Bob sees Anna at the front of her spaceship reach his doorway. At time zero on his clock, Bob Jr. sees the tail of Anna's spaceship at his doorway.

A) How fast is Anna's spaceship moving?
v/c = 0.781

L = Lo / Yv

--> 25 = 40 (square root) 1 - (v/c)^2

But how do you solve for v? I tried subtracting 25 and squaring it to get rid of the square root. But I just don't know how to get to v = 0.781 c

Thank you for any help

To solve for v, you need to rearrange the equation and isolate the square root term. Here's a step-by-step explanation of how to do it:

Start with the equation you provided:
25 = 40 * sqrt(1 - (v/c)^2)

1. Divide both sides of the equation by 40 to isolate the square root term:
25/40 = sqrt(1 - (v/c)^2)

2. Square both sides of the equation to eliminate the square root:
(25/40)^2 = 1 - (v/c)^2

3. Simplify the left side of the equation:
625/1600 = 1 - (v/c)^2

4. Subtract 1 from both sides of the equation to isolate the term with (v/c)^2:
-975/1600 = -(v/c)^2

5. Multiply both sides of the equation by -1 to get rid of the negative sign:
975/1600 = (v/c)^2

6. Take the square root of both sides of the equation to solve for (v/c):
sqrt(975/1600) = v/c

7. Evaluate the square root on the left side:
v/c = sqrt(975/1600)

8. Simplify the right side using a calculator:
v/c = 0.78125

So, the velocity of Anna's spaceship (v) is equal to 0.781 times the speed of light (c).