Question

In a kickball game, a ball is kicked and travels along a parabolic path. The height h, in feet, of the kickball t seconds after the kick can be modeled by the equation h(t) = −16 t2 + 24t .

a. A fielder runs a route that will allow him to catch the kickball at about 3 ft above the ground. Write an equation that can be used to find when the fielder will catch the ball.
b. Use graphing technology to find out how long the kickball has been in the air when the fielder catches it on its descent. Round to the nearest hundredth.

Answer 1

See below ~

Step-by-step explanation:

a. Equation

• In place of h(t), substitute 3 in its place
• 3 = -16t² + 24t
• Rearrange by bringing 3 to the other side
• -16t² + 24t - 3 = 0

b. Finding the duration of the kickball in air using graphing technology

• Based on the graph (attached), the ball has been in the air for :
• 1.5 seconds

Answer 2

(a) h(t) = 3

(b) time = 1.36 seconds

Step-by-step explanation:

equation: h(t) = -16(t)² + 24t

Part A

If the fielder catches the ball at the height of about 3 ft.

• equation: h(t) = 3

Part B

using graphing technology, graphed below. (height, y = 3)

Additional *solving part B algebraically*

-16(t)² + 24t = 3

-16(t)² + 24t - 3 = 0

using quadratic equation

`\bold{x = ( -b \pm √(b^2 - 4ac))/(2a) \ when \ ax^2 + bx + c = 0}`

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`\sf t_(1,\:2)=(-24\pm √(24^2-4\left(-16\right)\left(-3\right)))/(2\left(-16\right))`

`\sf t=(3-√(6))/(4), \ t=(3+√(6))/(4)`

t = 1.36 seconds and 0.14 seconds

The fielder shall catch the ball when the ball is falling, so time : 1.36 s