Equation of a circle word problem help?

Question

A rock is dropped into a pond, creating a circular ripple. The radius of the ripple increases steadily at 6 centimeters/sec. A toy boat is floating on the pond, 2.00 meters east and 1.00 meters north of the spot where the rock was dropped. How long does the ripple take to reach the boat? 

 

I understand that the equation of a circle is x²+y²=r², but I'm not sure how to apply it to this word problem. Thanks

Answer 1

You need to find out how far the boat is away from the rock.  That is found by

 

2²+1²=R² or R = SQRT(5) = 2.236 meters = 223.6 cm

 

Since the ripple is moving at  6 cm /sec:

 

223.6/6 = 37.267 seconds

Answer 2

The distance of the toy boat from the center is given by the Pythagorean Theorem:

 

distance = (x² + y²)^1/2 =  (2² + 1²)^1/2 = √5 m = 100√5 cm

 

The ripples move at 6 cm/sec.

 

distance = rate*time

 

distance/rate = time

 

(100√5 cm)/(6 cm/s) = (50√5)/3 s ≅ 37.27 s

Answer 3

Bianca,

 

This is more about a toy boat at a known distance from the center and a ripple moving to meet it at a constant rate. From Pythagorean theorem, we know the distance of the boat from where the rock was dropped is √(1^2+2^2)=√5. Then we set that to the rate of the growing ripple or 6t where t is in seconds.

√5=6t

t=.37s

 

Hope that helps!