A soccer ball rolls at $4 \mathrm{~m} / \mathrm{s}$ towards Marcos in a direct line from Michael. The ball is $15 \mathrm{~m}$ ahead of Michael who is chasing it at $9 \mathrm{~m} / \mathrm{s}$. Marcos is $30 \mathrm{~m}$ away from the ball and is running towards it at $8 \mathrm{~m} / \mathrm{s}$. The distance between Michael and Marcos when the ball is touched for the first time by one of them is closest to
(A) $2.00 \mathrm{~m}$
(B) $2.25 \mathrm{~m}$
(D) $2.75 \mathrm{~m}$
(E) $3.00 \mathrm{~m}$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-118.jpg?height=114&width=552&top_left_y=1862&top_left_x=1250)

## Part C: Each correct answer is worth 8.
The ball is rolling towards Marcos at $4 \mathrm{~m} / \mathrm{s}$ and he is running towards it at $8 \mathrm{~m} / \mathrm{s}$, so he gains 12 metres per second on the ball. Since he starts $30 \mathrm{~m}$ from the ball, it will take him $\frac{30}{12}=2.5 \mathrm{~s}$ to reach the ball.

The ball is rolling away from Michael at $4 \mathrm{~m} / \mathrm{s}$ and he is running at $9 \mathrm{~m} / \mathrm{s}$, so he is gaining 5 $\mathrm{m} / \mathrm{s}$ on the ball. Since he starts $15 \mathrm{~m}$ behind the ball, he would catch up to the ball in $3 \mathrm{~s}$ if it continued to roll.

Thus, Marcos gets to the ball first. After $2.5 \mathrm{~s}$, the Michael has gained $5(2.5)=12.5 \mathrm{~m}$ on the ball, so is $2.5 \mathrm{~m}$ from the ball when Marcos touches it first.

Answer: (C)

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