Question

It rises 18m every 3 s. After 5s, the drone is at a height of 40m, What is the initial value?

Answer 1

To find the initial value (the starting height) of the drone, we first need to determine the drone's rate of ascent and then apply this to the information we have about its height at 5 seconds.

The drone rises 18 meters every 3 seconds, which means its rate of ascent per second can be calculated as follows:

\[
\text{Rate of ascent} = \frac{18 \text{ m}}{3 \text{ s}} = 6 \text{ m/s}
\]

Now, at 5 seconds, the drone's height is given as 40 meters. The height of the drone at any time can be described by the formula:

\[
\text{Height} = \text{Initial Height} + (\text{Rate of ascent} \times \text{Time})
\]

Let \( h_0 \) represent the initial height.

We can set up the equation for the height at 5 seconds:

\[
40 = h_0 + (6 \, \text{m/s} \times 5 \, \text{s})
\]

Calculating \( 6 \, \text{m/s} \times 5 \, \text{s} \):

\[
6 \times 5 = 30 \text{ m}
\]

Now, substitute that back into the equation:

\[
40 = h_0 + 30
\]

To find the initial height \( h_0 \), we can rearrange the equation:

\[
h_0 = 40 - 30
\]

\[
h_0 = 10 \text{ m}
\]

Thus, the initial height of the drone is **10 meters**.