Science:Math Exam Resources/Courses/MATH110/April 2016/Question 06 (b)

MATH110 April 2016
Other MATH110 Exams

Question 06 (b)

A television camera is positioned ${\displaystyle 1000{\text{m}}}$ from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Answer the questions below. Make sure your solution includes a sketch that is labeled with the same variables used in your calculation. Your answer should be a numerical value, but you do not need to simplify it.

Assume the rocket rises vertically and its speed is ${\displaystyle 500{\text{m}}/{\text{s}}}$ when it has risen ${\displaystyle 2000{\text{m}}}$.

(b) If the television camera is always kept aimed at the rocket, how fast is the camera’s angle of elevation changing at that same moment?

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