Boat A negotiates a curve whose radius is 336 m. Boat B negotiates a curve whose radius is 160 m. Each boat experiences the same centripetal acceleration. What is the ratio of the speed of boat A to that of boat B?
To find the ratio of the speed of boat A to that of boat B, we can use the formula for centripetal acceleration:
a = (v^2) / r
Where:
- a is the centripetal acceleration
- v is the velocity/speed of the object
- r is the radius of the curve
Since both boats experience the same centripetal acceleration, we can equate their centripetal accelerations:
a(A) = a(B)
Plugging in the formulas for centripetal acceleration, we get:
(v(A)^2) / r(A) = (v(B)^2) / r(B)
Rearranging the equation to solve for the ratio of the speeds:
(v(A)^2) / (v(B)^2) = r(A) / r(B)
Now we can substitute the given values:
(r(A) / r(B)) = 336 m / 160 m = 2.1
Thus, the ratio of the speed of boat A to that of boat B is approximately 2.1:1.