Plot Range R vs Angle Theta (0-90)

[sally.smith4321]

We are given the velocity at which an object is projected (30 m/s) at an angle theta. I have to "Plot the range R as a function of angle theta (a value somewhere between 0 and 90 (including 0 and 90)). My thought was to possibly determine R using theta = 0 and theta = 90 to find a range, but I'm not sure that's right. The next question then asks "For what angle theta is the range R maximum?" How would I even find this?

 

[voko]

For any particular value of $\theta$, you have a particular range $R$. So you have a function: $R(\theta)$. You need to find a formula for this function and then do what you are asked.

 

[Dale]

Do you know how to find the maximum of a function?

 

[sally.smith4321]

Do you know how to find the maximum of a function?

No and I've read the chapter in my physics book twice, but still don't understand

 

[voko]

If the problem said, "find the range of a projectile launched at angle 21 degree to the horizontal with the initial velocity 30 m/s", how would you go about it?

 

[sally.smith4321]

If the problem said, "find the range of a projectile launched at angle 21 degree to the horizontal with the initial velocity 30 m/s", how would you go about it?

R(θ) = Vo2 sin(2θ)/g

R = (30^2 * sin(21))/9.8 = 32.91 m

 

[voko]

And now if the problem said the same, except "at angle 37 degree", I am sure you would be able to find the answer much in the same way, which is good. If you repeat that for a few different values of the angle, you will be able to plot the function. Just make sure that you cover the entire range 0 - 90 with values not too far away from each other. Does the plot suggest where the maximum might be?

 

[sally.smith4321]

And now if the problem said the same, except "at angle 37 degree", I am sure you would be able to find the answer much in the same way, which is good. If you repeat that for a few different values of the angle, you will be able to plot the function. Just make sure that you cover the entire range 0 - 90 with values not too far away from each other. Does the plot suggest where the maximum might be?

I solved using theta values = 0, 10, 20, and so on. It increased from R=0 to R=91.83 at theta=90. This was the highest value, but am I doing something wrong? If you shoot an object straight into the air, shouldn't it come straight down?

 

[Dale]

No and I've read the chapter in my physics book twice, but still don't understand

That is usually a topic that is covered in a math class. The way you do it is to take the derivative of the function and set it to 0. So here you would take $dR/d\theta=0$ and solve for $\theta$

 

[voko]

Your formula is correct. However, the results you are getting are not, because $\sin 2 \cdot 90^{\circ} = \sin 180^{\circ} = 0$. Check your calculations, and make sure your calculator is in the degrees mode.

 

[sally.smith4321]

Your formula is correct. However, the results you are getting are not, because $\sin 2 \cdot 90^{\circ} = \sin 180^{\circ} = 0$. Check your calculations, and make sure your calculator is in the degrees mode.

Okay! I forgot to multiply all of the numbers by 2! I'll do that now. Thank you so much for your help! You don't even understand how much it means to me!

 

[sally.smith4321]

That is usually a topic that is covered in a math class. The way you do it is to take the derivative of the function and set it to 0. So here you would take $dR/d\theta=0$ and solve for $\theta$

I'm in an algebra based calculus class. He doesn't want us using calculus. That's probably why we weren't taught the derivative part.