Question

A bee needs to fly to a flower 541 m due south of its hive. The bee’s speed in still air is

0.67 m/s, and there is a wind blowing toward the west at 0.2 m/s. What is the magnitude of the bee’s resultant velocity?

Answer 1

The resultant velocity of the bee, when considering its speed in still air and the wind's influence, is calculated using vector addition to be approximately 0.699 m/s.

Step-by-step explanation:

The student has asked about the resultant velocity of a bee that needs to fly to a flower 541 m due south of its hive while there is a wind blowing to the west. To calculate the magnitude of the resultant velocity, we need to consider the bee's speed in the absence of wind and the wind's speed as vectors and use vector addition.

In this scenario, the bee flies with a velocity of 0.67 m/s due south. The wind has a velocity of 0.2 m/s towards the west. Assuming east-west as the x-axis and north-south as the y-axis, the vectors are perpendicular to each other. The resultant velocity can be found using the Pythagorean theorem since we have a right triangle formed by the two velocity vectors. The magnitude of the resultant velocity (vR) is given by:

vR = √((vbee)2 + (vwind)2)
vR = √((0.67 m/s)2 + (0.2 m/s)2)
vR = √(0.4489 + 0.04)
vR = √(0.4889)
vR = 0.699 m/s (approximately)

Therefore, the bee's resultant velocity is approximately 0.699 m/s.