Energy and basic math (proportionality)

[Natko]

Homework Statement

A person running in a race has to pick up a mass equal to her own mass. Assuming she can still do the same
amount of work, her speed will be changed by a factor of
a. 0.25
b. 0.50
c. 0.71
d. 1
e. 2

Homework Equations

E=1/2mv²

The Attempt at a Solution

Since m is doubled, v² should be halved. I'm stuck now. But the correct answer is 0.71. Can someone explain how?

 

[goraemon]

Homework Statement

A person running in a race has to pick up a mass equal to her own mass. Assuming she can still do the same
amount of work, her speed will be changed by a factor of
a. 0.25
b. 0.50
c. 0.71
d. 1
e. 2

Homework Equations

E=1/2mv²

The Attempt at a Solution

Since m is doubled, v² should be halved. I'm stuck now. But the correct answer is 0.71. Can someone explain how?

You're correct that $v^2$ should be halved (multiplied by a factor of 1/2). So what does that say about the factor by which $v$ should be decreased?

 

[Natko]

You're correct that $v^2$ should be halved (multiplied by a factor of 1/2). So what does that say about the factor by which $v$ should be decreased?

Well, 1/2 squared is 0.25, and 1² halved is 0.5. How do I get to 0.71?

 

[goraemon]

Well, 1/2 squared is 0.25, and 1² halved is 0.5. How do I get to 0.71?

You know that her initial kinetic energy is $\frac{1}{2}mv_{0}^2$, the final kinetic energy is $\frac{1}{2}(2m)v_{1}^2$.

You need to find what the relationship between v1 and v0 is. Ask yourself, how can you do so given the above equations?

 

[Natko]

You know that her initial kinetic energy is $\frac{1}{2}mv_{0}^2$, the final kinetic energy is $\frac{1}{2}(2m)v_{1}^2$.

You need to find what the relationship between v1 and v0 is. Ask yourself, how can you do so given the above equations?

v₁² = ((1/2)v₀)²

If I let v₀ = 1, then v₁ = sqrt(1/2), which equals 0.71 :)

 

[goraemon]

v₁² = (1/2)v₀²

If I let v₀ = 1, then v₁ = 1/2, which doesn't work out.

That's not true. Check your math. As you state above, you've simplified the equation to the following:

$v_{1}^2=\frac{1}{2}v_{0}^2$

So just take the square root of both sides. What does that get you?

 

[Natko]

That's not true. Check your math. As you state above, you've simplified the equation to the following:

$v_{1}^2=\frac{1}{2}v_{0}^2$

So just take the square root of both sides. What does that get you?

Changed my previous post. Thanks!