346
Chapter 4 | Applications of Derivatives
Figure 4.4 (credit: modification of work by Steve Jurvetson, Wikimedia Commons)
A rocket is launched so that it rises vertically. A camera is positioned 5000ft from the launch pad. When the rocket is 1000ft above the launch pad, its velocity is 600 ft/sec. Find the necessary rate of change of the camera’s angle as a function of time so that it stays focused on the rocket.
Solution Step 1. Draw a picture introducing the variables.
Figure 4.5 A camera is positioned 5000 ft from the launch pad of the rocket. The height of the rocket and the angle of the camera are changing with respect to time. We denote those quantities with the variables h and θ , respectively.
Let h denote the height of the rocket above the launch pad and θ be the angle between the camera lens and the
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online