How Does Launch Angle Affect Projectile Range?

[Temper888]

1.1. Which of the following graphs BEST depicts the relationship between launch angle and range in the experiment?Please explain how you arrived to the answer.Attached is the graphs and the Experiment model.

Attached is the graphs and the Experiment model.The question is asking what happens to the range if the launch is increased? From equation R=v^2sin2θ/g, it can be said that range increases until the angle increases to 45 and then decreases from 45 and above because of sin2θ. The graph for range vs. launch angle should be a symmetrical upside-down parabola for same initial and final heights. However, I cannot figure out how does different initial and final heights as in this experiment affect the symmetry of that parabola?
3. I guessed it to be either Graph B or Graph C, but I am not sure.

 

[Simon Bridge]

Attached is the graphs and the Experiment model.

Try again - the attachments don't always get loaded.

The graph for range vs. launch angle should be a symmetrical upside-down parabola

Nope - it should be a sine curve... like the equation you quoted.
The graph of the trajectory should be a parabola, as should the height vs time curve.

However, I cannot figure out how does different initial and final heights as in this experiment affect the symmetry of that parabola?

Really? Then try doing some sample angles and plotting them out - this is what computers are good at after all. (Since ou have some example graphs, I bet you can find telltale characteristics.)

Thought experiment - if you fire at 90deg from the top of a cliff, your range is ______. How does that compare with the range at zero height? Repeat question for 0deg angle.