Chapter 3, Problem 3.76P

DATA A spring-gun projects a small rock from the ground with speed υ₀ try at an angle θ₀ above the ground. You have been asked to determine υ₀. From the way the spring-gun is constructed, you know that to a good approximation υ₀ is independent of the launch angle. You go to a level, open field, select a launch angle, and measure the horizontal distance the rock travels. You use g = 9.80 m/s² and ignore the small height of the end of the spring-gun’s barrel above the ground. Since your measurement includes some uncertainty in values measured for the launch angle and for the horizontal range, you repeat the measurement for several launch angles and obtain the results given in Fig. 3.76. You

Figure P3.76

ignore air resistance because there is no wind and the rock is small and heavy, (a) Select a way to represent the data well as a straight line, (b) Use the slope of the best straight-line fit to your data from part (a) to calculate υ₀. (C) When the launch angle is 36.9°, what maximum height above the ground does the rock reach?