eTutorialAssignmentaspx Home I Student madis Homework 3 Begin Date: 122/2018 12:

Question

eTutorialAssignmentaspx Home I Student madis Homework 3 Begin Date: 122/2018 12:00.00 AM-Due Date: 2122018 11:59.00 PM End Date: 2 (3%) Problem 10: An archer shoots an arrow at a target that is a hotzeetal dintiaced-6S m away, the bull'seye ofthe target is at same height as the release height of the arrow. Randomized Variables d-65m At what ar gle, in degrees above the honro tal, tut de are bereleased to hit the ball'seye if tal peed is 39 ms? eare i Grade Sammary Poteotial100 C0 co couo atanO ted Degrees C) Radars

Explanation / Answer

Given,

d = 65 m ; vi = 39 m/s

We need to have the range of 65 m

We know that, range is given by:

d = vx (2t)

t = vy/2g

vx = v cos(theta) ; vy = v sin(theta)

d = v cos(theta) x 2 v sin(theta)/2g

d = v^2 sin(theta) cos(theta)/g

trigonometric identity, sin(2theta) = sin(theta)cos(theta)

d = v^2 sin(2theta)/g

sin(2theta) = d g/v^2 = 65 x 9.8/39^2 = 0.4188

2theta = sin^-1(0.4188) = 24.76 deg

theta = 24.76/2 = 12.38 deg

Hence, theta = 12.38 deg

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