How long does the ripple take to reach the boat?

Question

The radius of the ripple increases steadily at 6 cm/sec. A toy boat is floating on the pond, 2.00 m east and 1.00m north. How long does the ripple take to reach the boat?

Answer 1

1) Use the distance formula to find the distance from the toy boat to the source of the ripple.  Pick the source of the ripple to be at coordinate (0.0).  The boat is at (2, 1).  D = √(2² + 1² =  √5 =  2.236m

 

2) The rate is 6cm/sec.  But since the coordinate is given in meters, convert 6 cm to .06m

 

3) The problem is asking for a time.  Use the formula T = D/R (where D = Distance, and R = rate)

Plugging in the numbers :  T = 2.236/.06 =  37.27 sec