# Projectile Motion range equation

1. Sep 23, 2015

### Kingyou123

1. The problem statement, all variables and given/known data
2. Relevant equations
x(t)=xo+v0xT+1/2axt^2
3. The attempt at a solution
(2Vo)costheta(t)=R, How would I get rid of T?

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2. Sep 23, 2015

### Staff: Mentor

Can you show how you arrived at your solution attempt? What does "costheta(t)" represent?

3. Sep 23, 2015

### Kingyou123

Velocity Intial of x is equal to vocostheta, should I be using range =(vo^2sin2(theta))/gravity. I'm really lost right now...

4. Sep 23, 2015

### Staff: Mentor

Okay, that's a bit better. The Range equation is a good approach. You should place the entire argument of a function within the parentheses to make it clear what the function argument is. Thus:

R = (vo2/g) sin(2θ)

(Note that you can use the $x_2$ and $x^2$ icons in the edit panel header to invoke superscripts and subscripts, and greek letters and other symbols can be selected from the $\Sigma$ icon's menu)

The range equation gives you the range of a projectile that's launched with a given velocity $v_o$ at a given angle $\theta$. So what happens to the range if you double the launch velocity?

For the second part of the question, take a browse though your table of trig identities then ponder what happens to sin and cos if the angle is adjusted as specified in the question.

5. Sep 23, 2015

### Kingyou123

Would it be 2R since the velocity is doubled?

6. Sep 23, 2015

### Staff: Mentor

Can you justify that with an argument based upon the range equation? I won't confirm or deny a guess...

7. Sep 23, 2015

### Kingyou123

I plugged 10 for the in initial velocity so doubling that would make 20/g therefore the outcome would be twice as great. Right logic or I'm I completely off/

8. Sep 23, 2015

### Staff: Mentor

It is not correct. Does the range equation use $v_o$ or $v_o^2$? How does squaring a doubled value affect the net result?

9. Sep 23, 2015

### Kingyou123

ohhhhhhh would it be 4R cause by doubling 1 you get 2 and 2^2 is 4 so in this case quadruplicating the R.

10. Sep 23, 2015

### Staff: Mentor

Bingo! It always pays to consider the equation involved and not rely on instinct alone

11. Sep 23, 2015

### Kingyou123

Thank you so much it makes so much more sense now :) Would you be up to help with the rest of homework when I get stuck?

12. Sep 23, 2015

### Kingyou123

For the second part would the angle be greater causing the distance to decrease? If I plug 30 in for theta, sin(90-30), the angle is greater than the previous 30, but if I plug 85 for theta the answer would less than...

13. Sep 23, 2015

### Kingyou123

Nevermind, sin(90-theta) is cos