Will give brainliest and extra points!! Aurora hit a baseball with an initial velocity of 70 feet per second at an angle of 30° with

Question

Will give brainliest and extra points!!
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.

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Thu Thủy 5 months 2021-09-05T16:56:26+00:00 1 Answers 2 views 0

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    2021-09-05T16:58:19+00:00

    Step-by-step Explanation:

    Given:

    v_0=70 \frac{ft}{s}

    \theta = 30°

    Let’s consider the point where the baseball was hit to be the origin of our coordinate system. The equation for the y-motion of the baseball can be written as

    y= -16t^2 + v_{0y}t=-16t^2 + (70 \sin30°)t

    or

    y=-16t^2 + 35t

    a) In order to find the time of flight of the baseball, we know that it will hit the ground when y=-3\:ft so we can rewrite the equation for as follows:

    -3 = -16T^2 + 35T \rightarrow 16T^2 - 35T - 3 = 0

    where T is the time of flight. Solving for the roots of the quadratic equation, we get

    T = \dfrac{35 \pm \sqrt{(-35)^2 - 4(16)(-3)}}{2(16)}

    \:\:\:\:\:\:= \dfrac{35 \pm 32.14}{32} = 2.10\: s\:\: \text{or}\:\: 0.09\:s

    We take the t=2.10 \:s as the time it takes for the baseball to hit the ground.

    b) We know that the horizontal distance traveled by the baseball is given by

    x=(v_0 \cos 30°)T=(70\:\frac{ft}{s})(0.866)(2.10\:s)

    or

    x = 127.31 ft

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