How do I calculate work in two-dimensions and find the final velocity and time?

[Edel Crine]

Homework Statement

Starting from rest, an intern pushes a 45-kg gurney 40 m down the hall with a constant force of 80 N directed downward at an angle of 35° with respect to the horizontal.
(a) What is the work done by the intern on the gurney during the 15-m trip?
(b) How fast is the gurney going when it has moved 15 m?
(c) How much time elapses during the 15-m journey? Ignore friction.

Relevant Equations

W=F*x

I'm not sure that does the given distance represent "x" direction? If so, I did...

a) Fx = 80N * cos(35°) = 65.53N
W = F*Δx = 65.53N * (15m) = 982.98 J

b) k = 982.98 J = 1/2 (m)(v2)
v = (√2k/m) = 6.6 m/s

c) vf = vi + at

a = F/m = 1.46 m/s2

t = (vf-vi)/a = 4.54 sec

But I'm not sure for I got... h

 

[haruspex]

The problem statement says 40m, but then asks about 15m. Which is it?

 

[Edel Crine]

The problem statement says 40m, but then asks about 15m. Which is it?

Well, the problem statement said 40m, but subproblems said 15m, so I think we need to solve it by 15m?

 

[sysprog]

I think that the problem may be hinting at the law of cosines regarding the 35° slope.

 

[Edel Crine]

I think that the problem may be hinting at the law of cosines with respect to the 35° slope.

yeah, I think so too and that's how I did...?

 

[haruspex]

Well, the problem statement said 40m, but subproblems said 15m, so I think we need to solve it by 15m?

Sounds to me like a recycled problem. The question setter failed to update all the parts.
You have answered correctly for 15m, except that you quote too many significant figures. The given data only provides two.

 

[sysprog]

yeah, I think so too and that's how I did...?

It looks that way to me, but I think that @haruspex and others here are more expert on this than I am .

 

[Edel Crine]

Sounds to me like a recycled problem. The question setter failed to update all the parts.
You have answered correctly for 15m, except that you quote too many significant figures. The given data only provides two.

Oh yes, I almost forgot about it...hh 'Appreciate!

 

[Edel Crine]

It looks that way to me, but I think that @haruspex and others here are more expert on this than I am .

You are good! I appreciate every comment from you hh