Science:Math Exam Resources/Courses/MATH100 B/December 2023/Question 11
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 • Q12 • Q13 • Q14 • Q15 • Q16 • Q17 • Q18 • Q19 • Q20 • Q21 • Q22 • Q23 • Q24 • Q25 • Q26 • Q27(a) • Q27(b) • Q27(c) • Q28(a) • Q28(b) • Q29(a) • Q29(b) • Q30(a) • Q30(b) • Q30(c) • Q30(d) • Q30(e) • Q30(f) •
Question 11 

A car is driving at m/s along a straight road. A police officer is standing m to the side of the road with a radar gun measuring speeds. The measured speed is the rate of change of the distance between car and officer. What is the measured speed when the car has not yet passed the officer and is 3m away from the closest point on the road to the officer? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Draw a picture! This is a related rates question. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Consider the picture below. Note that it is drawn at the point in time when is 3, but must remember to treat as a function of time. The quantity that we are looking for is the rate of change of the distance between the car and the police officer, when the car is m away from the point on the road closest to the officer (labelled ). We need to come up with an equation for how changes with respect to the distance , from the car to point . This is given through the relation where and are both functions of time. Using implicit differentiation, we can find Now, substituting in , , we have m/s, so the speed at which the distance is changing at this point in time is 12m/s. 