Question

"An electric toy airplane is flying in a horizontal circle of radius R = 15 meters. If it takes the plane 5 seconds to go around the circle, how fast is it going?

A. 6 m/s
B. 15 m/s
C. 30 m/s
D. 75 m/s"

Answer 1

To find the speed of the toy airplane, calculate the circumference of the circle using the formula C = 2πR and then divide by the period (time for one complete circle). The speed comes out to approximately 18.84 m/s, but due to an error in the provided options, the closest answer would be 30 m/s (option C).

Step-by-step explanation:

To find out how fast the electric toy airplane is going while it is flying in a horizontal circle with a radius R of 15 meters, we need to calculate its velocity. The airplane completes one circle in 5 seconds, so its period (T) is 5s. The circumference of the circle, which is the distance the airplane travels in one full circle, is given by C = 2πR. Plugging in the value for R:

C = 2π × 15 m

C = 30π m

To find the speed (v), we divide the distance by the time taken for one complete circle:

v = C / T

v = (30π m) / 5 s

v = 6π m/s

Since π is approximately equal to 3.14, the speed is approximately:

v ≈ 6 × 3.14 m/s

v ≈ 18.84 m/s

However, as this is not an option provided, it looks like there's an error in the options given to the student. If we strictly consider the closest number to the actual answer, the answer would be:

C. 30 m/s