A seagull drops a sea urchin onto the rocks below from a height of 80 m . The
function models the height of the urchin, in metres, and is the time in
seconds. When will the sea urchin hit the rocks?

Ask by Huff Ortega. in Canada

Nov 20,2024

Question

A seagull drops a sea urchin onto the rocks below from a height of 80 m . The
function models the height of the urchin, in metres, and is the time in
seconds. When will the sea urchin hit the rocks?

Ask by Huff Ortega. in Canada

Nov 20,2024

UpStudy AI · Accepted Answer

To find out when the sea urchin hits the rocks, we need to determine when the height $$ h(t) $$ is equal to 0. The height function is given by:

$$
h(t) = -5t^2 + 80
$$

We set this equal to 0 to find the time $$ t $$ when the sea urchin hits the rocks:

$$
-5t^2 + 80 = 0
$$

Now, we can solve for $$ t $$:

1. Rearrange the equation:

$$
-5t^2 = -80
$$

2. Divide both sides by -5:

$$
t^2 = \frac{80}{5} = 16
$$

3. Take the square root of both sides:

$$
t = \sqrt{16} = 4
$$

Since time cannot be negative, we take the positive root:

$$
t = 4
$$

Thus, the sea urchin will hit the rocks after **4 seconds**.
The sea urchin will hit the rocks after 4 seconds.