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Romero Hamilton
05/28/2023 · Middle School

Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of \( 39.2 \mathrm{~m} / \mathrm{s} \) from a height of 161.7 m above the ground. The height (in meters) of the stone above the ground \( t \) seconds after it is thrown is \( \mathrm{s}(\mathrm{t})=-4.9 \mathrm{t}^{2}+39.2 \mathrm{t}+161.7 \). a. Determine the velocity v of the stone after t seconds. b. When does the stone reach its highest point? c . What is the height of the stone at the highest point? d. When does the stone strike the ground? e. With what velocity does the stone strike the ground? f. On what intervals is the speed increasing?

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a. \( v(t) = -9.8t + 39.2 \) b. Highest point at \( t = 4 \) seconds c. Height at highest point: \( 240.1 \) meters d. Strikes ground at \( t \approx 11 \) seconds e. Velocity when striking ground: \( -68.6 \) m/s f. Speed increasing on the interval \( (4, 11) \) seconds

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