Union College Winter 2016

Physics 120: Lab 3 (Measurements of Launch Speed) Worksheet

Name: ______Partners: ______

1) Derivation of initial velocity of ball:

a) Maximum height: Consider a ball that starts at position <0, yi, 0> and is given an initial velocity <0, vi, 0>. What will its highest position, < 0, ymax, 0 >? Recall that the peak of a projectile’s motion occurs when vy = 0. (Since all the x and z values stay = 0, you can solve using only the y-components.)

Rearrange the equation to give an expression for vi in terms of y(= ymax – yi).

vi =

b) Time of flight: Consider a ball starting at position < 0, yi, 0 > with initial velocity < 0, vi, 0 >, and ending at position < 0, 0, 0 >. Derive an expression for the initial speed, vi, in terms of the initial height, yi, and the time duration, t, for the ball to complete this motion.

Rearrange the equation to give an expression for vi in terms of t.

vi =

2)Which method do you expect to give better results and why?

a) What are some possible sources of systematic error and of random error in measuring the maximum height reached by the ball? How will you remove the systematic error?

b) What are some possible sources of systematic error and of random error in timing the motion of the ball? Will your reaction time be a source of random error, or of systematic error?

c) Estimate your reaction time (in seconds)______. Describe how you came up with that estimate.

3) Number of launcher : ______

4) For the maximum height measurements, what is the initial position?

yi = ______

5) For the time of flight measurements, what is the initial position?

yi = ______

6) Estimated uncertainties:

(y) ~ ______(t) ~ ______

Data:

Time Trial / Time of Flight(s) / Height Trial / Height (m)
1 / 1
2 / 2
3 / 3
4 / 4
5 / 5
6 / 6
7 / 7
8 / 8
9 / 9
10 / 10

Calculations:

Average time:______Average Height______

Partners’:______Partners’:______

Standard Deviation (t) ______Standard Deviation: (h):______

Partners’: ______Partners’: ______

Comparison of standard deviation with estimated uncertainties:

Average height ± standard error for group: ______

Standard Error (t): ______Standard Error (h): ______

tavg± t: ______havg± h: ______

Partners’: ______Partners’: ______

Comparisons:

Average time ± standard error for group: ______

Launch Speed:

Vlaunch from average height: ______

Average Vlaunch of individual calculations: ______

Standard deviation of Vlaunch: ______

Standard error: ______

Avg Vlaunch ± standard error from height measurements: ______

comparison withVlaunch from average height:

Vlaunch from average time: ______

Average Vlaunch of individual calculations: ______

Standard deviation of Vlaunch: ______

Standard error: ______

Avg Vlaunch ± standard error from time measurements:: ______

comparison withVlaunch from average time:

Comparison of results using heights and results using times:

Horizontal Launch:

Derivation ofEquation for predicted distance in terms of initial velocity:

Predicted distance from height measurements:

Predicted distance (using vave+ 2*standard error) =

Predicted distance (using vave - 2*standard error) =

Predicted distance from time measurements:

Predicted distance (using vave + 2*standard error) =

Predicted distance (using vave - 2*standard error) =

Result: How far did the ball land?

Which method for measuring the initial velocity is this more consistent with? Explain Is this the method you thought would be more accurate? Make a justification why the other method is not as accurate.