Introduction to Computational Physics Homework 5: Projectile Motion with Air Resistance, Assignments of Physics

Download Introduction to Computational Physics Homework 5: Projectile Motion with Air Resistance and more Assignments Physics in PDF only on Docsity! PHYS 105: Introduction to Computational Physics Spring 2009 Homework #5 (Due: May 21, 2009) 1. Do in-class exercise 7.1. Turn in your program (part 2) and three plots (parts 4 and 5), and clearly state the results you obtain in response to the other questions asked. 2. Consider again a projectile moving in two dimensions under the combined effects of gravity and air resistance. Initially the projectile is launched from x = 0, y = 0 with speed v0 = 100 m/s at an angle of θ0 = 60 ◦ to the horizontal. The components of its acceleration are ax = −β |v| vx , ay = −g − β |v| vy , where β = 0.001 (chosen so that the initial acceleration for this value of v0 is the same as the case α = 0.1 in problem 1). (a) Compute the projectile’s range and time of flight (take δt = 0.01, and don’t forget to interpolate!), and compare them to the results of the α = 0.1, β = 0 calculation in problem 1. Plot both trajectories (α = 0.1, β = 0 and α = 0, β = 0.001) on the same graph. (b) At what angle to the horizontal θ1 does the projectile hit the ground in either case in part (a)? What would θ1 be in the absence of air resistance (i.e. α = β = 0)? (c) By what factor (to within 1 percent) must the launch speed for α = 0, β = 0.001 be increased to restore the range to the α = β = 0 result? (d) By varying the value of θ0, determine the maximum range of the projectile for v0 = 100 m/s (again with α = 0, β = 0.001). To what value of θ0 (to 1 decimal place) does this correspond? (e) For v0 = 100 m/s, plot θ1 as a function of θ0. 3. Now suppose that the value of β in problem 2 varies with height y, according to the law β(y) = 0.001e−y/h , where h = 500 m (not a very realistic description of Earth’s atmosphere!). How does the maximum range of the projectile (as computed in problem 2d) change as a result? What if h = 5 km (a much better approximation to reality)?