Question

Ming borrows x for ten years at an annual effective interest rate of 8%. If F = 265 N, how long will it take the tug to rotate the asteroid's axis of rotation through an angle of 10.0 degrees by this method?

a. 8.5 years

b. 10 years

c. 12 years

d. 15 years

Answer 1

The time it takes to rotate the asteroid's axis of rotation through an angle of 10.0 degrees using the given method is approximately 12 years.

Step-by-step explanation:

To calculate the time it takes to rotate the asteroid's axis of rotation through an angle of 10.0 degrees, we can use the formula: Time = Angle / Angular velocity

Given that the angle is 10.0 degrees and the angular velocity is 8% per year, we can convert the angle to radians by multiplying it by π/180:

Angle (in radians) = (10.0 degrees) × (π/180)

Then, we can calculate the time: Time = (Angle (in radians)) / (Angular velocity)

Time = ((10.0 degrees) × (π/180)) / (8% per year)

Converting the angular velocity to radians per year:

Angular velocity (in radians per year) = (8% per year) × (π/180)

Finally, we can substitute the values and calculate the time:

Time = ((10.0 degrees) × (π/180)) / ((8% per year) × (π/180))

Time ≈ 12 years