Question

17. A bottlenose dolphin jumps out of the water. The path the dolphin Travels can be
modeled by h = -0.2d2 + 2d, where h represents the height of the dolphin and d
represents horizontal distance.
a. What is the maximum height the dolphin reaches?
b. How far did the dolphin jump?

Answer 1

Answer:

a. 5 units

b. 5 units

Step-by-step explanation:

Given:

The path the dolphin Travels can be  modelled by $h = -0.2d^2 + 2d$ where  h represents the height of the dolphin and d  represents horizontal distance.

To find: maximum height that the dolphin reaches and the distance covered by dolphin

Solution:

$h = -0.2d^2 + 2d$

Differentiate with respect to $d$

$\frac{\mathrm{d} h}{\mathrm{d} d}=-0.4d+2$

To find the critical point, put $\frac{\mathrm{d} h}{\mathrm{d} d}=0$

$d=\frac{2}{0.4}\\=\frac{20}{4}\\=5 \,\,units$

Differentiate $\frac{\mathrm{d} h}{\mathrm{d} d}$ again with respect to $d$

$\frac{\mathrm{d^2} h}{\mathrm{d} d^2}=-0.4<0$

So, $d=5$ is a point of maxima

$h(5) = -0.2(5)^2 + 2(5)\\=-0.2(25)+10\\=-5+10\\=5\,\,units$

a. 5 units

b. 5 units