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During halftime of a football game, a sling shot launches T-shirts at the crowd A T-shirt is launched from a height of 6 feet with an initial upward velocity of 72 feet per second Use the

equation h(t) = -16 +72t+6, where t is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height?

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Answer:

Hope this helps ;)

Explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

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