Question

An ant starts at one edge of a long strip of paper that is 34.2 cm wide. She travels at 0.4 cm/s at an angle of 52◦ with the long edge. How long will it take her to get across? Answer in units of s.

Answer 1

The ant travels at an angle with a vertical component of speed, and it will take approximately 108.54 seconds to cross the 34.2 cm-wide strip of paper.

Step-by-step explanation:

To determine how long it takes the ant to cross the strip of paper, we need to understand the relationship between the angle of travel, the width of the paper, and the ant's speed.

The width of the paper is given as 34.2 cm, and the angle at which the ant is traveling is 52 degrees to the long edge of the paper. The ant's speed is 0.4 cm/s. To find the time it takes to cross, we use the formula for the vertical component of the ant's velocity: speed * sin(angle).

Time to cross = Width of paper / Vertical component of speed
Time to cross = 34.2 cm / (0.4 cm/s * sin(52 degrees))
Time to cross = 34.2 cm / (0.4 cm/s * 0.7880)
Time to cross = 34.2 cm / 0.3152 cm/s
Time to cross = 108.54 seconds

The ant will take approximately 108.54 seconds to cross the 34.2 cm-wide strip of paper.

Answer 2

`t=108.50s`

Step-by-step explanation:

The ant is under an uniform motion. So, we get the time taken by the ant to cross the strip from the definition of speed:

`v=(x)/(t)\\t=(x)/(v)`

In this case, we use the vertical speed of the ant (
`v_y=vsin\theta`), since the ant crosses the strip that is 34.2 cm wide (vertically). So:

`t=(y)/(v_y)\\t=(y)/(vsin\theta)\\t=(34.2cm)/(0.4(cm)/(s)sin(52^\circ))\\t=108.50s`