Find final speed using mechanical energy formula

[Angela_vaal]

Homework Statement

A skateboarder at a skate park rides along the path shown in (Figure 1) .If the speed of the skateboarder at point A is v=1.3m/s, what is her speed at point B? Assume that friction is negligible.

Homework Equations

u_i+k_i=u_f+k_f
u=mgh
k=1/2mv²

The Attempt at a Solution

m(9.8x2.7)+1/2m(1.3)²=m(9.8x1)+1/2mv_f²
m(26.46+.845)=m(9.8+.5) mv_f²
v_f=√((26.46+.845)/(9.8+.5))
answer=1.6 m/s
The answer is wrong. Can somebody please tell me what I am doing wrong? Thanks!

 

[TomHart]

Looks like you changed 0.845 to 8.45 from one step to the next. That could have caused a problem but I didn't verify that was it.

 

[Angela_vaal]

Looks like you changed 0.845 to 8.45 from one step to the next. That could have caused a problem but I didn't verify that was it.

I wrote it down wrong here but I did the work using.845 and still got 1.6m/s. I don't know what I am doing wrong :(

 

[TomHart]

I'll look at it again.

 

[TomHart]

Yeah, you have a math problem in going from the first line to the second line. You should re-work that again carefully.

 

[Angela_vaal]

Yeah, you have a math problem in going from the first line to the second line. You should re-work that again carefully.

I will do that right now.

 

[Angela_vaal]

I"m not that great at math. Can you give me a hint of what I did wrong?

 

[TomHart]

@Angela_vaal you wrote:
m(9.8x2.7)+1/2m(1.3)²=m(9.8x1)+1/2mv_f²
It's okay that you didn't, but at this point you could have (probably should have) canceled out all of the m's, because each term contains an 'm'.

Then you wrote:
m(26.46+.845)=m(9.8+.5) mv_f²
I'm not exactly sure what you did to get to this equation. It looks like you're trying to factor mv_f² out of both terms on the right-hand side of the equation, but the first term does not contain a v_f². So that was not legal.

I think you ought to factor out all of the 'm's in the first equation, multiply out the numbers, and that will [hopefully] make it clearer to see how to proceed.

 

[ehild]

Homework Equations

u_i+k_i=u_f+k_f
u=mgh
k=1/2mv²

The Attempt at a Solution

m(9.8x2.7)+1/2m(1.3)²=m(9.8x1)+1/2mv_f²
m(26.46+.845)=m(9.8+.5) mv_f²

The RHS should be 9.8m+0.5 mv_f²
Factor out m.

 

[Kaura]

Yeah I think it is just a math error as the general method of solving looks fine

 

[Angela_vaal]

I figured it out thank you!