## 4200.24 – Rocket Launch

You are 2 km from the launch pad, watching a mighty rocket climb skyward, under the fearless command of the intrepid Captain Navarchus. Your first observation gives an angle of elevation of 21 degrees. Five seconds later, you observe that the angle has increased to 35 degrees. What was the rocket's average speed during the five-second interval?

## Solution

We want the rate of change of $x$ as shown on the diagram below. Distances are in meters; time is in seconds. It is simplest to note that $x$ is the difference in the rockets height at the two observations, so,

$x = 2000 \tan{35°}- 2000 \tan{21°} \approx 633.$

This distance is covered in 5 seconds so the rate on average is $633/5 \text{ m/s} \approx 127\text{ m/s}$.