Question

The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at a height of 5 feet? round your answers to the nearest tenth.

Answer 1

Answer:

The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.

Step-by-step explanation:

Given : The function $h=-16t^2+26t$models the height h (in feet) of the dolphin after t seconds.

To Find: After how many seconds is the dolphin at a height of 5 feet?

Solution:

Function: $h=-16t^2+26t$

h is the height

t is the time

Now we are supposed to find After how many seconds is the dolphin at a height of 5 feet

Substitute h = 5

So, $5=-16t^2+26t$

$16t^2-26t+5=0$

$16t^2-26t+5=0$ ---1

Using quadratic formula : $x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

General quadratic equation: $ax^2+bx+c=0$   ---A

On Comparing equation 1 with A

a = 16

b = -26

c=5

Substitute the values in the quadratic formula.

$x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}$

$x = \frac{26\pm 18.86796}{32}$

$x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}$

$x = 1.4021,0.2228$

Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.

Answer 2

Given the movement of Dolphin has been modeled by the function:
h(t)=-16t^2+26t
the time taken for Dolphin to reach 5 feet will be:
5=-16t^2+26t
writing the above in quadratic form ax^2+bx+c=0 we get:
16t^2-26t+5=0
solving the quadratic equation using quadratic formula we obtain:
t=13/16+/-√89/16
t=0.22 sec or 1.40 sec