Question

A speedboat negotiates a curve whose radius is 120 m. What is the speedboat's speed if it completes the curve in 10 seconds?

1) 20 m/s
2) 24 m/s
3) 30 m/s
4) 36 m/s

Answer 1

To find the speed of the speedboat, you can use the formula for centripetal acceleration. Using the given radius of the curve and the time it takes to complete the curve, you can calculate the speed of the speedboat to be approximately 34.64 m/s.

Step-by-step explanation:

To find the speed of the speedboat, we need to use the formula for centripetal acceleration, which is given by:

a = v^2 / r

Where:
- a is the acceleration
- v is the speed
- r is the radius of the curve

Since we know the radius of the curve (120 m) and the time it takes to complete the curve (10 seconds), we can solve for the speed:

a = v^2 / r

v^2 = ar

v = sqrt(ar)

Substituting the values gives:

v = sqrt((10 m/s^2) * (120 m))

v = sqrt(1200 m^2/s^2)

v = 34.64 m/s

Therefore, the speed of the speedboat is approximately 34.64 m/s.