Question

A carnival game involves striking a lever that forces a weight up a tube. If the weight

reaches 20 feet to ring the bell, the contestant wins a prize. The function h(t) = -16t2 +
32t + 3 gives the height of the weight at any given time.
1. Find the maximum height of the weight.
2. How many seconds will it take for the weight to reach the maximum height?
3. Will the contestant win a prize?
pls answer

Answer 1

1. 19 ft
2. 1 second
3. no prize

Explanation:

The given equation for ballistic motion graphs as a parabola that opens downward. When the equation is graphed using a graphing calculator, the graph shows the weight reaches a maximum height of 19 ft after 1 second. Since the weight does not reach 20 feet, there is no prize.

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The time at the vertex of the function h(t) = at^2 +bt +c is given by t=-b/(2a). For the given function that time is ...

t = -(32)/(2(-16)) = 1

The height at t=1 is ...

h(1) = -16(1^2) +32(1) +3 = 19

The vertex is (t, h) = (1, 19).

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1. The maximum height is 19 feet

2. It takes 1 second for the weight to reach the maximum height.

3. The contestant will not win a prize.