# Long jump velocity question

1. Jul 14, 2006

### kristen151027

I have what probably sounds like a simple question...here it is:

You desperately want to qualify for the Olympics in the long jump, so you decide to hold the qualifying event on the moon of your choice. You need to jump 7.52 m (and conveniently beat Galina Chistyakova's record) to qualify. The maximum speed at which you can run at any location is 5.90 m/s. What is the magnitude of the maximum rate of freefall acceleration the moon can have for you to achieve your dream?

equations:
∆x=-v^2sin2Φ/a_y
Φ = 0.5arcsin [-a_y∆x/v^2]
there are other equations but I don't know which ones to use

Last edited: Jul 14, 2006
2. Jul 14, 2006

### arunbg

Do you know projectile motion analysis ?

Hint: Use the equation for maximum range .

3. Jul 14, 2006

### kristen151027

We've been studying projectiles, but nothing too indepth. I tried to use the first equation I listed (the maximum range one...?), but I ran into trouble with the angle measurement.

4. Jul 14, 2006

### arunbg

At what angle does the projectile or jumper attain maximum range ?

5. Jul 14, 2006

### kristen151027

No idea...is that something the question should provide?

6. Jul 14, 2006

### arunbg

In your first expression, ∆x becomes max. when sin2Φ = 1.
Therefore Φ equals ___ ?

7. Jul 14, 2006

### kristen151027

Φ = 45 degrees
(because sin2Φ = 2sinΦcosΦ
and when Φ = 45 ... it's 2*(1/root 2)*(1/root 2)...which is 1)
if Φ = 45 degrees, then the a_y = -4.63 m/s^2
therefore, the magnitude is 4.63
correct?

8. Jul 14, 2006

### kristen151027

One thing I'm not quite clear on is how "∆x becomes max. when sin2Φ = 1" ...I'm probably just not thinking clearly about it. The answer is asking for the magnitude, not the direction, so the sign of the answer doesn't matter.

9. Jul 14, 2006

### arunbg

Yes, you are right
Edit: What are the values that sine function can take ?

10. Jul 14, 2006

### kristen151027

The sine function can take values of 0 to 1. Ah and it can't be 0, so one is the maximum, but when sinx = 1, cosx = 0. Therefore, it has to be somewhere in between. Now the question is how to indicate such logic concisely when doing a problem. (I very much appreciate your help, by the way!!!)

Edit: sine can take values of -1 to 1...oops

Last edited: Jul 14, 2006
11. Jul 14, 2006

### kristen151027

Just got it. When Φ = 45 degrees, that's creates the maximum value because we're dealing with a double-angle. So that explains why the answer is highest when Φ = 45 degrees.