A grandfather pulls his granddaughter, whose mass is 20.5 kg

[AD_3]

Homework Statement

A grandfather pulls his granddaughter, whose mass is 20.5 kg and who is sitting on a swing with ropes of length 2.57 m, backward and releases her from rest. The speed of the granddaughter at the bottom of the swinging motion is 2.61 m/s. What is the angle (in degrees, measured relative to the vertical) from which she is released?

Homework Equations

P=F*V
W=F*d

The Attempt at a Solution

I don't even know were to start with this. I feel it has something to do with work or power but I can't figure it out. I first tried Fcosθ=V but that didn't work

 

[tvavanasd]

...

Homework Equations

P=F*V
W=F*d
...

Along with work, have you studied potential and kinetic energy?

 

[jedishrfu]

Well she had potential e when her grandfather held her at some angle and when she was at the bottom she can't swing any lower and she's moving so she's got kinetic e so what can you deduce from that?

 

[tvavanasd]

Everything.
The angle isn't really important yet.
How about calculating the initial starting height (potential) based on the known kinetic energy.
Can you list both the potential and kinetic energy equations?

 

[AD_3]

You are right I overlooked those equations. I know KE=.5mv^2 and I think PE=mgh. Is the PE when the grandfather holds her equal to the KE at the bottom?

 

[tvavanasd]

Yes, when the grandfather holds her at the top, all energy is potential. Assuming negligible loss to drag and friction, at the bottom of the swing motion all energy should be kinetic.

 

[AD_3]

So once I set those equal and solve for h do I use sin(theta)=o/h to solve for theta?

 

[tvavanasd]

It's a little tougher than that. Draw a diagram showing the swing rope length, height change and theta.
Note that:
h used in potential energy equations is change in height.
h used in trig is hypotenuse.
For clarity (and to avoid confusion), consider using "hyp" for hypotenuse.
I think that you will find that you should use cosine rather than sine.
Give it a try and see how far you get.

 

[AD_3]

Oh okay I understand. Thank you! I got 30.1 deg