Question

A carnival attraction tests your strength by how far in the air you can drive a weight with a hammer. If the weight reaches 15 feet, you win a prize. The equation h = -16t 2+ 31t + 2 gives the height, in feet, and time, in seconds of the weight after it is hit.

a. How long is the weight in the air?
b. What was the weight’s maximum height?
c. Did you win a prize? Why or why not?

Answer 1

• a. 2 seconds
• b. ~17 feet
• c. yes

Explanation:

Given function:

• h(t) = -16t² + 31t + 2

a.

h(t) = 0 will give us the y-intercept of the graph. The greater value of t is the time the weight in the air

• -16t² + 31t + 2 = 0
• 16t² - 31t - 2 = 0
• t = [31 + √(31²+4*16*2)]/32
• t = (31 + 33)/32
• t = 2 seconds

b.

Maximum height is reached at vertex.

The x coordinate of the vertex is determined as x = -b/(2a), considering the standard form of a quadratic function f(x) = ax² + bx + c

• t = -31/(-16*2) = 31/32 = 0.96875
• h(0.96875) = -16(0.96875)² + 31*0.96875 + 2 = 17.015625 ft

c.

• You win the prize as the maximum height is greater than 15 feet