Homework Help: 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