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Aurora hit a baseball with an initial velocity of 70 feet per second at an angle of 30° with the horizontal. The ball hit her bat when the ball was 3 feet above the ground.

(a) No one interferes with the ball. How long does it take the ball to hit the ground? Round your answer to the nearest hundredth of a second. Show all your work.

(b) How far did the ball travel horizontally? Use your answer from Part (a) in your calculations. Round your answer to the nearest tenth of a foot. Show all your work.

 Apr 20, 2020
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a)
initial velocity in the y direction = v0sinθ = 70sin(30°)=35m/s
bc of symmetry and parabola stuff, final velocity in the y direction = -35m/s

use v=v0+at, solve for t ---> t = (v-v0)/a = (-35m/s-35m/s)/(-9.8m/s2) = 7.14286s = 7.14s

b)

initial velocity in the x direction = v0cosθ = 70cos(30°)=60.62178m/s

you found the time it takes to hit the ground in part a, so use that in this equation:
d = vt, where d = distance/displacement, 
d = 60.62178m/s * 7.14286s = 433.01ft

 Apr 20, 2020

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