# Homework Help: Finding minimum velocity.

1. Oct 30, 2011

### Miike012

What is the minimum speed the rock must have, when it leaves the sling to travel exactly 400 m?

The only equation I can think of using is...

y = (tan(theta initial))x - (g/(2Vx0^2)x^2

y = 0
x = 400
However I have to many unknowns... I need to solve for V but I dont know Vx0 or Vy0 or the initial angle...

Help would be appreciated... thank you.

2. Oct 30, 2011

### sandy.bridge

You should post the entire question as it is relatively difficult to help with what you have given.

3. Oct 30, 2011

### sandy.bridge

If that is all you are given, note that
$$v_{min}$$ will occur when $$\theta =\frac{\pi}{4}$$

4. Oct 30, 2011

### Miike012

That was all I was given

5. Oct 30, 2011

### Miike012

Why will this be a 45 deg angle?

6. Oct 30, 2011

### Miike012

Ok I got the answer correct.. but can some one please tell me why initial theta is 45 deg?

7. Oct 30, 2011

### sandy.bridge

Proof:
Use the range equation,
$$R = \frac{V_{i}^2 sin 2\theta}{g}$$
Solve this equation for the initial velocity. Then treat it like a max/min problem and differentiate the equation, set equal to zero and solve. You will determine that the minimum occurs at 45 degrees.

8. Oct 30, 2011

### Miike012

interesting... I probably dont know that because I am not in a calc based phy

9. Oct 30, 2011

### Miike012

is that the only way to determine the 45 deg angle by differentiating?

10. Oct 30, 2011

### Miike012

and how can the range equation be used for this type of problem? The range equation I thought only deals with situations when a projectile travels some horizontal distance before falling to its original position... but in the case of the problem I posted the object would have fallen to its original position, that being the ground at y = 0.

11. Oct 30, 2011

### sandy.bridge

I merely presented the range equation as a method for proving that the minimum occurs at 45 degrees. Moreover, now that you know the angle is 45 degrees, you can plug and chug into any equations that apply for this problem.

12. Oct 30, 2011

### Miike012

do i differentiate Initial V with respect to initial theta and keep R constant?

13. Oct 30, 2011

### sandy.bridge

Yes, dv/dθ

14. Oct 31, 2011

### Redbelly98

Staff Emeritus
No, it's not the only way. You (should) know that sin(anything) has a maximum value of 1, which happens when "anything" is equal to ____?

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