Two steamrollers begin 105 mm apart and head toward each other, each at a constant speed of 1.20 m/s. At the same instant, a fly that travels at a constant speed of 2.50 m/s starts from the front roller of the southbound steamroller and flies to the front roller of the northbound one, then turns around and flies to the front roller of the southbound once again, and continues in this way until it is crushed between the steamrollers in a collision.

Required:
What distance does the fly travel?

Answer: 109.4 mm

Explanation: Distance is a scalar quantity and it is the measure of how much path there are between two locations. It can be calculated as the product of velocity and time:  d = vt

The separation between the two steamrollers is 105 mm or 0.105 m. They collide to each other at the middle of the separation:

location of collision = [tex]\frac{0.105}{2}[/tex] = 0.0525 m

To reach that point, both steamrollers will have spent

[tex]v=\frac{\Delta x}{t}[/tex]

[tex]t=\frac{\Delta x}{v}[/tex]

[tex]t=\frac{0.0525}{1.2}[/tex]

t = 0.04375 s

The fly is travelling with speed of 2.5 m/s. So, at t = 0.04375 s:

d = 2.5*0.04375

d = 0.109375 m

Until it is crushed, the fly will have traveled 109.4 mm.

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