Problem

A ball is thrown from an initial height of 4 feet with an initial upward velocity of 29ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=4+29t16t2
Find all values of t for which the ball's height is 16 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answer

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Answer

Final Answer: The ball is at a height of 16 feet at times t=0.64 seconds or t=1.17 seconds.

Steps

Step 1 :Given the equation for the height of the ball is h=4+29t16t2, we need to find the time t when the height h is 16 feet. This means we need to solve the equation 4+29t16t2=16 for t.

Step 2 :This is a quadratic equation, and we can solve it using the quadratic formula t=b±b24ac2a, where a, b, and c are the coefficients of the quadratic equation at2+bt+c=0. In this case, a=16, b=29, and c=416=12.

Step 3 :Substituting the values of a, b, and c into the quadratic formula, we get two solutions for t, which are t1=1.17 and t2=0.64.

Step 4 :Final Answer: The ball is at a height of 16 feet at times t=0.64 seconds or t=1.17 seconds.

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