# Projectile questions

1. Dec 6, 2015

### Hashiramasenju

1. The problem statement, all variables and given/known data

whats the minimum angles to the vertical(theta) for a projectile(ball) to be realeased with speed v such that at any point of time the distance to the ball is increasing.
2. Relevant equations

Sh=vtsin(theta)
Sv=vtcos(theta)-0.5gt^2

3. The attempt at a solution
so i used pythagoras theorum to find the square of the distance to the projectile(R). thus d(R^2)/dt>0 because the distance to the ball from the origin(start point) must be increasing. But the algebra gets really nasty. Is there any alternative way or is there any error in my method
Thanks

2. Dec 6, 2015

### Simon Bridge

No, thats pretty much it. You probably need a table of trig substitutions.
Don't forget you only need dR/dt > 0 for 0 < t < T (time of flight)... in fact, if R decreases at all, which part of the trajectory will that happen?

There are other methods... ie you can guess some values and look for a pattern, you can try using your understanding of parabolas to narrow your choice, use graphing software... etc.

Last edited: Dec 6, 2015
3. Dec 6, 2015

### Hashiramasenju

Btw is the answer 45 deg

4. Dec 6, 2015

### Hashiramasenju

So is the answer 45 deg and 35.26

5. Dec 6, 2015

### Simon Bridge

The question only requires one number for the answer.
I don't know the correct answer off the top of my head.

6. Dec 6, 2015

### SammyS

Staff Emeritus
I get something a bit less than 20° .

7. Dec 7, 2015

### Hashiramasenju

How did you get that ?

8. Dec 7, 2015

### SammyS

Staff Emeritus
I did what you set up as follows.
R2 = Sh2 + Sv2 is not as difficult to deal with as it might at first appear to be. R2 is a degree 4 polynomial in t, but the constant term and the linear term are bot zero. Its derivative is a cubic polynomial in t, with a constant term of 0, so that one of the zeros is t=0, and you can use the quadratic formula for the other two zeros.

All that is needed is that the derivative is never zero, except perhaps at t = 0. Simply check the discriminant to determine those conditions.