Question

Estimate the time at which the cyclists pass each other?Cyclist A sets off at 10 m from the starting position and gets to 60m in 10 seconds.Cyclist B sets off from 60 meters away at 0 seconds at in 10 seconds get to the starting position.Estimate the time at which the two cyclists pass each other?

Answer 1

Given:

• Cyclist A:

Starting position = 10 m

Gets to 60 m in 10 seconds

• Cyclist B:

Starting position = 60 m at 0 seconds

Gets to starting position in 10 seconds

Let's estimate the time at which the two cyclists pass each other.

Let's find the velocity of each cyclist:

Velocity of cyclist A:

$s=\frac{\Delta x}{t}=\frac{60-10}{10}=\frac{50}{10}=5\text{ m/s}$

Velocity of cyclist B:

$s=\frac{\Delta x}{t}=\frac{0-60}{10}=\frac{-60}{10}=-6\text{ m/s}$

Now, let's write the motion of each cyclist as an equation:

Cyclist A: y = 5x + 10

Cyclist B: y = -6x + 60

Where x represents the time and y is the position.

Now, let's solve both equations simultaneously:

$5x+10=-6x+60$

Now, let's solve for x.

Move all terms with the variable x to the left

$\begin{gathered} 5x+6x=60-10 \\ \\ 11x=50 \\ \text{ } \\ \text{ Divide both sides by 11:} \\ \frac{11x}{11}=\frac{50}{11} \\ \\ x=4.54 \end{gathered}$

Therefore, the time at which the two cyclists will pass each other is 4.54 seconds

• ANSWER:

4.54 seconds