A person stands 303030 meters east of an intersection and watches a car driving away from the intersection to the north at 171717 meters per second. At a certain instant, the car is 161616 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)?

3.9973.997 meter/second

Step-by-step explanation:

In other to determine the rate of change of distance between the man and the car at that instant, the component of speed of the car along the line joining the person and the car must be determined.  

We know that The person was standing 12 meter east of intersection and the car is 9 meters north of the intersection. If we interpret this using the four cardinal point we will see that it produce a right triangle straight away with sides of length 12 and 9cm, now we will need to denote the length of the third sides of the triangle with x. Which can then be solved using Pythagoras theorem.

By Pythagoras theorem:

c=√(a² + b²)

x= √(12² + 9²)  

x = 15 meters  

Speed along north direction was given as 4 meters/second  

Rate of change of the distance between the car and the person which is the speed along the line joining both of them  

= 4Cos(p)  

=4 cos(9/15)  

=3.9973.997 meter/second  

Hence, the rate of change of the distance between the car and the person which is the Speed along the line joining both of them is 3.9973.997 meter/second.

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