Question

Bumblebees are skilled aerialists, able to fly with confidence around and through the leaves and stems of plants. In one test of bumblebee aerial navigation, bees in level flight flew at a constant 0.40 m/s, turning right and left as they navigated an obstacle-filled track. While turning, the bees maintained a reasonably constant centripetal acceleration of 4.0 m/s2.

What is the radius of curvature for such a turn?
How much time is required for a bee to execute a 90 degree turn?

Answer 1

The radius of curvature is 0.04 meters and it would take 9 seconds for the bee to execute a 90 degree turn.

Step-by-step explanation:

To find the radius of curvature for the turn, we can use the formula:

r = v²/a

where r is the radius of curvature, v is the velocity, and a is the centripetal acceleration.

Substituting the given values:

r = (0.40 m/s)² / (4.0 m/s²) = 0.04 m

Therefore, the radius of curvature for the turn is 0.04 meters.

To determine the time required for the bee to execute a 90 degree turn, we can use the formula:

t = θ / ω

where t is the time, θ is the angle of rotation, and ω is the angular velocity.

Since the bee is executing a 90 degree turn, θ = 90°.

Substituting the given value for the velocity:

ω = v / r = (0.40 m/s) / (0.04 m) = 10 rad/s

Substituting the values into the formula:

t = 90° / (10 rad/s) = 9 seconds

Therefore, it would take the bee 9 seconds to execute a 90 degree turn.