Hello, these are 4 questions on a lab that I had to do for a review, yet I don\'

Question

Hello, these are 4 questions on a lab that I had to do for a review, yet I don't understand what they are asking, it is possible that no background info is needed besides the graph and the equation that I posted in the picture. Yet in case that more information is needed, please read the "Key info". Thank you very much for any if at all any help that you can possibly give me. Thank you. And sorry if it's a mess or it makes no sense.

Key info: For this experiment, you will be given a ball launcher and a ball bearing.First we will understand the horizontal launch versus the drop by using our ball launcher with on ball bearing on each side of the launcher, this was recorded into high speed. After doing so we came up with the hypothesis that "A ball launched at a positive angle will be in the air longer and have a higher maximum height than a ball launched at angle launched lower than it". The video as placed into a program that measured the speed as filmed in high speed (as shown in the graph of dots). This meassured how the angle of the launch affected the x and y components of the initial velocity, assuming that our x axis is horizontal, and y is vertical.

4(a) How do you derive the general formula for total time of flight as it depends on your launch angle? Assume y to be the vertical axis, and motion to be in the x-y plane. v0 is the magnitude of your initial velocity, and g = 9.8 m/s2.

4(b) If y = y0, how does the equation in 4(a) simplify?

4(c) How would you use this expression of t (from 4(a)) to get an expression of range (final displacement in the x-direction)?

4(d) Looking at the graph from 2(d), you may see that some values of x have two launch angles associated with it. What can you infer from this?

Explanation / Answer

4 a) http://physics.bu.edu/~duffy/semester1/c4_timeflight.html 4 c) http://www.ux1.eiu.edu/~cfadd/1150/03Vct2D/proj.html

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