4200.24 – Rocket Launch

Tags:Problem Set 6Pre-Calculus MathTrigonometry

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?


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

x=2000tan35°2000tan21°633.x = 2000 \tan{35°}- 2000 \tan{21°} \approx 633.

This distance is covered in 5 seconds so the rate on average is 633/5 m/s127 m/s633/5 \text{ m/s} \approx 127\text{ m/s}.