# Very simple question

1. May 26, 2005

### eNathan

$$.0834 = .5 \sqrt { 1 - v^2 }$$

What is $$v^2$$?

2. May 26, 2005

### dextercioby

Square both terms and isolate v^2...

Daniel.

3. May 26, 2005

### eNathan

can you explain?

4. May 26, 2005

### dextercioby

$$(0.0834)^2 =(0.5)^2 \left(1-v^2 \right)$$

Divide by 0.25.

Daniel.

5. May 26, 2005

### mathwonk

it seems to be about 35/36 just off the top of my head.

6. May 26, 2005

### HallsofIvy

Staff Emeritus

Explain what? Do you know how to square a number? Do you know what $$$$\sqrt{1- x^2}$$^2$$ is?

Although I would be inclined to multiply both sides of the equation by 2 first.

7. May 26, 2005

### JoshHolloway

I would have divided both sides by 1/2 first. then squared both sides.

8. May 27, 2005

### eNathan

Ok, let me ask it in a simpler form.

If $$L_t = \sqrt {1 - \frac {v^2} {c^2} }$$ then what does $$v^2$$ equal? BTW is it posible for the explination to be in the form of an anctual equation?

Thx

9. May 27, 2005

### dextercioby

There's no explanation that could be given by an equation.Explaining means putting words,describing a method...

Daniel.

10. May 27, 2005

### dx

$$c^2 ( 1 - L^2 )$$

Last edited: May 27, 2005
11. May 27, 2005

### eNathan

you can explain things using an equation by studying it, hence understanding it.

In any case, I have one more questionair. It seems I have forgot to include the LT factor in the equation.

If $$T = t \sqrt {1- \frac {v^2} {c^2} }$$ then what is $$v^2$$

12. May 27, 2005

### eNathan

Ok, I think it is
$$v^2 = c^2 \frac {(1-T^2)} {t}$$

13. May 27, 2005

### jdavel

Nope. Try again.

14. May 27, 2005

### mathwonk

another casualty of the epidemic decline of algebra skills since the introduction of the hand held calculator, and MTV, and the republican controlled congress, and daylight savings time, and fluoridation of the water, and the new deal, and.....oops time for my medication.

15. May 27, 2005

### eNathan

J338!5 I though physicsforums.com was to help people, not talk about the decline in inteligence.

--Nuf Said

16. May 27, 2005

### TenaliRaman

eNathan,
the simplified equation you were after was
v^2 = c^2 (1 - (T^2/t^2))

-- AI

17. May 27, 2005

### whozum

You forgot to mention the introduction of baby pickles!

18. May 27, 2005

### whozum

Since the answer has been provided I'll show you how.

$$T = t\sqrt{1-\frac{v^2}{c^2}}$$

Divide both sides by t

$$\frac{T}{t} = \sqrt{1-\frac{v^2}{c^2}}$$

Square both sides

$$\left(\frac{T}{t}\right)^2 = 1-\frac{v^2}{c^2}$$

Subtract one from both sides, then since the right side is negative, multiply both sides by negative one.

$$1-\left(\frac{T}{t}\right)^2 = \frac{v^2}{c^2}$$

Multiply both sides by c^2

$$c^2\left(1 - \frac{T^2}{t^2}\right) = v^2$$

19. May 27, 2005

### eNathan

Derived! Makes perfect sense, thx a lot for the explinationair

20. May 27, 2005

### whozum

You should definitely brush up on your algebra. It's essential to your science career.