# Homework Help: Projectile difficult

1. Jun 1, 2013

### rattanjot14

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

1. Find the maximum angle of projection of a projectile such that its position vector from the origin to the subsequent position of the projectile is always increasing.

2. Relevant equations

3. The attempt at a solution
x(t)=v*cos(A)t, y(t)=v*sin(A)t-(1/2)gt^2. v is the initial velocity, A is the angle from the horizontal.
then x^2 +y^2 =k^2
We know that k^2 should always be increasing then we would differentiate it w.r.t to time and put it ≥ 0. But the problem is that i am getting two times for it. now what to do..?

2. Jun 1, 2013

### voko

If you get some values of t, that means the magnitude of displacement will be increasing sometimes. You must find a condition when it always increases.

3. Jun 1, 2013

### rattanjot14

i have a doubt when i differentiate it wrt to time i assume that theta is constant. can i do that..??

4. Jun 1, 2013

### voko

Does the initial angle of projection change as time goes on?

5. Jun 1, 2013

### rattanjot14

but we had to find the maximum angle of projection..

6. Jun 1, 2013

And?

7. Jun 1, 2013

### rattanjot14

only angle of projection for which the position vector always increases..

8. Jun 1, 2013

### voko

You don't have to repeat the problem.

9. Jun 1, 2013

### rattanjot14

so is it correct to assume it constant..?

10. Jun 1, 2013

### voko

11. Jun 1, 2013

### rattanjot14

thnx answer is coming sin inverse 1/u

12. Jun 1, 2013

### voko

I do not think this is correct. Show how you got that.

13. Jun 1, 2013

### rattanjot14

r^2 = (u^2)t + (g^2)(t^4) - (usinθ)gt^3
differentiating it and putting it equal to 0 we get
(gt)^2 -3usinθgt +2u^2 =0
so t = (3usinθ ± √9u^2sin^2θ-8u^2)/20
and also this time ≤2usinθ/g (total time of flight)]
solving this i dont get the answer...i was getting that because of an error.
now what to do?

14. Jun 1, 2013

### voko

Explain how you got (u^2)t in r^2 = (u^2)t + (g^2)(t^4) - (usinθ)gt^3.

15. Jun 1, 2013

### rattanjot14

typing error it is . the actual it is

(u^2)t^2 + [(g^2)(t^4)/4] - (usinθ)gt^3.

16. Jun 1, 2013

### voko

So how can one ensure that (gt)^2 -3usinθgt +2u^2 is ALWAYS greater than zero?

17. Jun 1, 2013

### rattanjot14

if d is less than or equal to zero.

18. Jun 1, 2013

### rattanjot14

19. Jun 1, 2013

### rattanjot14

is that correct?

20. Jun 1, 2013

### voko

This is not yet the answer. But you are on the right track.