What is the optimal angle for achieving maximum range

Assignment Help Engineering Mathematics

Reference no: EM131860270

Assignment -

A. Investigate the effect of backspin and dimples on the motion of a golf ball. In this case, assume that the initial velocity is 70 m/s. The effect of dimples on a golf ball can have a significant effect on the range of the ball.

For this case assume that C_d = 0.5 for speeds up to 14 m/s and C_d =7.0/v for higher speeds.

For the Magnus force, use Sω₀/m ≈ 0.25 s^-1.

The mass of a golf ball is 0.04593 kg and its radius is 3 cm.

Plot a few sample trajectories for different launch angles.

What is the optimal angle for achieving maximum range?

Compare that to the results for a smooth ball where C_d is constant C_d =0.5.

[Computer. Turn in the program, results and 2 plots for the smooth versus non-smooth ball. Be sure to label your plots.]

In question (A), modify your range program to compute the range for a golf ball.
To find the correct optimal angle, make sure you sample a large range of angles.

Pendulums -

1. In the small angle approximation, the total energy of a simple pendulum is

E = ½mL²ω²+ ½mgLθ² - mgL

Show analytically that E monotonically increases with time when the Euler method is used to compute the motion. [Pencil]

2. Write a version of the pendul program that uses:

(a) the Euler-Cromer method

(b) the Leap-Frog method

Run your program for the cases in figures 2.7 - 2.8 of the text. Compare your results with the Euler and Verlet methods. A table of input parameters is shown below.

Figure number	Initial angle θ₀ (degrees)	Timestep τ (sec.)	Number of steps
2.7	10	0.1	300
2.8	170	0.1	300

Attachment:- Assignment Files.rar

Reference no: EM131860270

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