Projectile Motion range equation

[Kingyou123]

Homework Statement

Uploaded

Homework Equations

x(t)=xo+v0xT+1/2axt^2

The Attempt at a Solution

(2Vo)costheta(t)=R, How would I get rid of T?

 

[gneill]

Homework Statement

Uploaded

Homework Equations

x(t)=xo+v0xT+1/2axt^2

The Attempt at a Solution

(2Vo)costheta(t)=R, How would I get rid of T?

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

 

[Kingyou123]

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

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

 

[gneill]

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

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 = (v_o²/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.

 

[Kingyou123]

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 = (v_o²/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.

Would it be 2R since the velocity is doubled?

 

[gneill]

Would it be 2R since the velocity is doubled?

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

 

[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/

 

[gneill]

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/

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?

 

[Kingyou123]

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?

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

 

[gneill]

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

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

 

[Kingyou123]

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

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?

 

[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?

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...

 

[Kingyou123]

Nevermind, sin(90-theta) is cos