Question

Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. When the frisbee is thrown, it follows a parabolic path that is modeled by the function h(t) = – 0.145t2 + 0.019t + 5.5. How many seconds will it take for the frisbee to hit the ground?

–6.2 seconds
–6.1 seconds
5.5 seconds
6.2 seconds

Answer 1

• D. 6.2 seconds

Explanation:

When the frisbee hits the ground, the value of h is zero.

Find the time required:

• – 0.145t² + 0.019t + 5.5 = 0
• 145t² - 19t - 5500 = 0
• t = (19 + √(19² + 4*145*5500))/290 = (19 + 1786,1)/290 = 6.2 seconds (rounded)
• Note, taking positive root only as time is never negative

Answer 2

6.2 seconds

Explanation:

Given function: h(t) = – 0.145t² + 0.019t + 5.5

• Here h(t) which determines the height, when Frisbee touches the ground, the height shall be 0.

solve the quadratic equation:

using the formula:
`\left[\begin{array}{ccc} t = ( -b \pm √(b^2 - 4ac))/(2a)\end{array}\right]`

Solving steps:

→ –0.145t² + 0.019t + 5.5 = 0

→ [–0.145t² + 0.019t + 5.5 = 0 ]* 100

→ -145t² + 19t + 5500 = 0

→
`t = ( -19 \pm √(19^2 - 4 ( -145)(5500)))/(2(-145))`

→
`t_1=(-19+√(3190361))/(2\left(-145\right)),\:t_2=(-19-√(3190361))/(2\left(-145\right))`

→
`t = -6.09` ,
`t = 6.2`

→
`t = 6.2`

Time cannot be negative here.

• So time taken: 6.2 seconds.