Question

You cast a fishing lure from 4 feet above the water. Its travel is given by the function h = -16t^2 + 24t + 4, where t = time in seconds. After how many seconds will it reach a height of 12 feet?

Answer 1

Answer:

Fishing lure will be at a height of 12 feet after 0.19 and 1.31 seconds

Step-by-step explanation:

Travel of a fishing lure has been given by the expression,

h = -16t + 24t + 4

where h = height of the fishing lure

t = time or duration of travel

Height traveled by the fishing lure = 12 - 4 = 8 feet

For h = 8 feet,

8 = -16t² + 24t + 4

-16t² + 24t + 4 - 8 = 0

16t² - 24t + 4 = 0

4t² - 6t + 1 = 0

t = $\frac{6\pm\sqrt{(-6)^{2}-4(4)(1)}}{2\times 4}$

 = $\frac{6\pm\sqrt{36-16}}{8}$

 = $\frac{6\pm\sqrt{20}}{8}$

 = $\frac{6\pm2\sqrt{5}}{8}$

 = 1.31, 0.19 seconds