The speed for a basketball that is dropped from a helicopter is given by where g

ID: 1730443 • Letter: T

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The speed for a basketball that is dropped from a helicopter is given by where g (gravity) = 9.81 m / s2, C (drag coefficient "drag") = 0.5, p = 1.2m3 -9k which is the density of the air, the projected area of the ball A = pi*r2. Use r = 0.117 m radius.
a. Re write the equation to find the value of the mass in kg so that in 5 seconds it achieves 19.5 m / s of speed. b. Write a program using the 4 methods studied in class that for each case write the solution, the number of iterations, the relative error and the real error using as real value in long format the value obtained with fzero in Matlab. Allow a tolerance of 0.0001. where g (gravity) = 9.81 m / s2, C (drag coefficient "drag") = 0.5, p = 1.2m3 -9k which is the density of the air, the projected area of the ball A = pi*r2. Use r = 0.117 m radius.
a. Re write the equation to find the value of the mass in kg so that in 5 seconds it achieves 19.5 m / s of speed. b. Write a program using the 4 methods studied in class that for each case write the solution, the number of iterations, the relative error and the real error using as real value in long format the value obtained with fzero in Matlab. Allow a tolerance of 0.0001. mg PA C

Explanation / Answer

solution

a) by substituting the values of g,p.A andC we can write the equation as in the form

v=27.577(m)1/2(1-exp(-0.334t/(m)1/2)

at t=5s the v=19.5 m/s then equation is

19.5=27.577(m)1/2(1-exp(-1.77/(m)1/2

The expansion exp(-x)=1- x + x2/2 +…………

Here we can avoid high order terms because x is a fractional quantity

So the equation is 0.71= (m)1/2 (1-(1-x+ x2/2)) where x=0.167/(m)1/2

0.71=(m)1/2(1.77/(m)1/2)(1-1.77/(m)1/2)

1.77/(m)1/2= 1.77-.71=1.06 which gives m= (1.77/1.06)2 =2.81kg

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The speed for a basketball that is dropped from a helicopter is given by where g

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