# Crossing the Paper Strip: How Long Will the Ant Take?

## What is the scenario of the ant crossing a long strip of paper?

An ant starts at one edge of a long strip of paper that is 34.2 cm wide. She travels at 1.3 cm/s at an angle of 61◦ with the long edge. How long will it take her to get across?

## Answer:

The ant will take 30.1 seconds to cross the paper strip.

When an ant starts at one edge of a long strip of paper that is 34.2 cm wide and travels at a speed of 1.3 cm/s at an angle of 61° with the long edge, we can calculate the time it takes for the ant to cross the paper strip.

To find the time taken, we need to determine the component of the ant's velocity that is across the paper. This can be calculated by finding the projection of the velocity vector along the axis perpendicular to the long edge of the paper. In this case, the component of velocity across the paper (vₓ) can be calculated using the formula vₓ = v * sin(θ), where v is the magnitude of the velocity (1.3 cm/s) and θ is the angle (61°).

By substituting the values into the formula, we get:

vₓ = 1.3 cm/s * sin(61°) = 1.3 cm/s * 0.875 = 1.14 cm/s

Now, to find the time taken for the ant to cross the paper strip, we can use the formula for average velocity: t = distance / velocity

Distance = 34.2 cm (width of the paper strip) and velocity across the paper (vₓ) = 1.14 cm/s

Therefore, t = 34.2 cm / 1.14 cm/s = 30.1 seconds

So, it will take the ant approximately 30.1 seconds to cross the long paper strip at the given speed and angle.