Question

Mr. jones is a hiker and likes going on adventures all the time. Besides hiking,he dives periodically from a height above a swimming pool. The function h(t) = -5t^2+10t+15 is used systematically to model his height above the water in feet at a time "t" seconds after diving. Diving from a Plank Board, what time does it take him to reach the maximum height? what is the maximum height?

Answer 1

Answer: the time it takes for Mr. Jones to reach the maximum height is:

t = -b/2a = -10/(2*(-5)) = 1

Explanation:

Answer 2

it takes Mr. Jones 1 second to reach the maximum height of 45 feet when he dives from a plank board.

Explanation:

To find the time when Mr. Jones reaches the maximum height, we need to find the vertex of the parabola represented by the function h(t). The vertex of a parabola is given by the formula (−b/2a,h(−b/2a)), where a and b are the coefficients of the t

2

and t terms, respectively.

In the case of the function h(t), a=−5 and b=10, so the vertex is located at (−10/2(−5),h(−10/2(−5))=(1,45) seconds. Therefore, it takes Mr. Jones 1 second to reach the maximum height.

The maximum height is simply the y-coordinate of the vertex, which is 45 feet.

In conclusion, it takes Mr. Jones 1 second to reach the maximum height of 45 feet when he dives from a plank board.