Finding velocity for half-rate time dilation and half-length contraction

[erok81]

Homework Statement

I have a two part question where one has to solve for a velocity to make a moving clock run half the rate as one at rest. Then the second part is what velocity would an object have to move in order to make its length halved.

Homework Equations

$$t'=t\gamma$$

$$L=\frac{L_{0}}{\gamma}$$ where L0 is the object at rest.

$$\gamma=\frac{1}{\sqrt{1-\beta^{2}}}$$

The Attempt at a Solution

I chose gamma to be equal to two. That way, using my equations above, the time would run slower by half and the length the same.

Is this an incorrect way of thinking for this problem? I have both problems with the same velocity, 0.86c. I thought it kind of odd that a two part question would have the same answer so I am really doubting what I've solved for.

Am I close?

 

[nickjer]

You are correct. Maybe their goal was to make you second guess yourself :)