# Homework Help: Hooke's Law - help please

1. Sep 17, 2014

### aatgomez

In preparing to shoot an arrow, an archer pulls a bowstring back 20 cm=.2 m. The arrow can reach a horizontal distance of 300 m and the arrow weighs 200 g. Find k.

m=.2 kg
W=1/2kd final- 1/2kd initial
Fs=-kx

Not really sure where to begin, and I've been trying for a while now.

2. Sep 17, 2014

### Staff: Mentor

There are squares missing in your second equation.

To shoot 300m, how fast does the arrow have to be initially? And what is the ideal angle to shoot the arrow, neglecting air resistance?

3. Sep 17, 2014

### aatgomez

oh yes, sorry W=1/2kd^2 final - 1/2kd^2 initial
It would have to be 0 initially and I'm thinking 45 degrees?

4. Sep 17, 2014

### Staff: Mentor

45 degrees is right. With "initially", I meant the flight path, so directly after it leaves the bow. If it is too slow, it won't make 300 meters, obviously.

5. Sep 17, 2014

### aatgomez

Ok, so if I find the initial velocity and the final velocity as if I were doing projectile problem then I can find W=1/2mvf^2 - 1/2mvi^2 then I could set W equal to 1/2kd^2 final - 1/2kd^2 initial and find k. Is that correct?

6. Sep 17, 2014

### Staff: Mentor

No. The energy from the spring does not get "used up" in the flight. It is still in the arrow when it hits the ground.

The velocity is the key connection here.

7. Sep 17, 2014

### aatgomez

I see that there's potential energy before the arrow is shot. That's where the .2 m come in. But I still don't know how to solve it. A little more help please?

8. Sep 17, 2014

### Staff: Mentor

Find the velocity the arrow needs to fly 300m. Once you have that, the rest should follow from that velocity. Note that is the same hint I gave in post #2.

9. Sep 17, 2014

### aatgomez

Right I realize that, that's what I don't know how to find.

10. Sep 17, 2014

### Staff: Mentor

The arrow is in free fall. Maybe the opposite problem is easier: If you know the initial velocity and angle, how far will it go?
I'm quite sure you have solved a problem of this type before in your course or as homework.