A lightning bug flies at a velocity of 0.25m/s due east toward another lightning bug seen off in the distance. A light breeze blows from the east on the bug at a velocity of 0.25m/s. What is the resultant velocity of the lightning bug?

Please direct me to even start-I'm totally lost

The question is confusing because it does not make clear if the 0.25 m/s is the velocity with respect to the ground or the air.

Presumably the bug is flying through air at 0.25 m/s (the so-called "air speed") and the air is blowing in the opposite direction at 0.25 m/s.

That would make the resultant velocity (with respect to the ground) zero.

0 m/s

damn if i know

To solve this problem, we need to understand vector addition and how to calculate resultant velocity.

Vector addition involves adding two or more vectors to determine a single vector called the resultant vector. In this case, we need to determine the resultant velocity of the lightning bug considering both its own velocity and the velocity of the breeze.

To get started, let's break down the given information into vectors:

1. Velocity of the lightning bug flying due east: 0.25 m/s east → (0.25 m/s, 0 m/s)
2. Velocity of the breeze blowing from the east: 0.25 m/s west ← (-0.25 m/s, 0 m/s)

Now, we can add these two vectors to find the resultant velocity. To add the vectors, we sum their corresponding components:

Resultant Velocity = (0.25 m/s + (-0.25 m/s), 0 m/s + 0 m/s)

Simplifying the addition:

Resultant Velocity = (0 m/s, 0 m/s)

The resultant velocity of the lightning bug is 0 m/s in the horizontal (east-west) direction, meaning there is no net movement in that direction due to the bug's own velocity and the breeze canceling each other out. The bug's velocity and the breeze velocity are equal but opposite, resulting in a net horizontal velocity of zero.