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Onodeyja
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Homework Statement
A player located 18.1 ft from a basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle Θ = 34 degrees and initial velocity of v = 25 ft/s.A. Show that the distance s of the shot changes by approximately 0.255∆Θ ft if the angle changes by an amount ∆Θ. Remember to convert the angle to radians in the Linear Approximation.
B. Is it likely that the shot would have been successful if the angle were off by 2 degrees?
Homework Equations
s = (1/32)v² * sin(2Θ)
The Attempt at a Solution
I'm not sure if I'm going in the right direction, but here's what I have.
∆f = f'(a)∆Θ
f' = 1250/32 * cos(2Θ)
∆f = f'(34 * (∏/180)) * ∆Θ
∆f = 1250/32 * cos(2 * (17∏/90)) * ∆Θ
∆f = 1250/32 * cos (17∏/90) * ∆Θ
∆f = 32.38∆Θ = 0.255
∆Θ = 0.255/32.38 = 0.00787 * (180/∏) = 0.45˚
Part B: No, the shot wouldn't be successful.
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