(5%) Problem 16: A soccer ball is kicked from ground level across a level soccer

Question

(5%) Problem 16: A soccer ball is kicked from ground level across a level soccer field with initial velocity vector vo-9 m s at 30° above horizontal. The soccer ball feels wind resistance which causes it to slow horizontally with constant acceleration magnitude ax 0.76 m/s', while leaving its vertical motion unchanged. Assume any other air resistance is negligible. Choose the positive direction of x from initial point towards final point of flight. Use a Cartesian coordinate system with the origin at the ball's initial position. 50% Part (a) The ball travels through the air until it returns to the soccer field. Calculate the ball's time of flight, trin seconds. 50% Part (b) Calculate the horizontal distance. xmar in meters, the ball travels before it returns to the soccer field

Explanation / Answer

from the equation s = ut+1/2at^2

vertical equation

y(t) = 0 = -1/2*9.8*t^2+9tsin36

-4.9t^2+5.29t = 0

4.9t^2 = 5.29t

t = 5.29/4.9 = 1.08 sec

b) x(t) = 9tcos36-1/2*0.76t^2 = 7.28 t-0.38t^2

at t = 1.08 sec

x = 7.42 m

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