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The problem describes a stone being thrown vertically upwards with an initial velocity of \( 7.0 \, \text{m/s} \), and asks for the velocity of the stone when it is at a height of \( 2.0 \, \text{m} \) above its starting position.

We can solve this problem using the **conservation of mechanical energy** or the **kinematic equations**. In this case, I will use the kinematic equation for vertical motion:

\[
v^2 = u^2 - 2gh
\]

Where:
- \( v \) is the final velocity at height \( h \) (this is what we're solving for),
- \( u = 7.0 \, \text{m/s} \) is the initial velocity,
- \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity (taking the downward direction as positive),
- \( h = 2.0 \, \text{m} \) is the height above the starting point.

### Let's calculate the final velocity \( v \).

\[
v^2 = (7.0)^2 - 2 \times 9.8 \times 2.0
\]

\[
v^2 = 49 - 39.2 = 9.8
\]

\[
v = \sqrt{9.8} \approx 3.13 \, \text{m/s}
\]

Therefore, the velocity of the stone at a height of 2.0 meters is approximately **3.13 m/s**. This is closest to option **C: 3.0 m/s**.

Would you like more details or have any questions?

Here are five related questions:
1. How would the velocity change if the initial velocity was higher, say 10 m/s?
2. What would the velocity be if the stone was thrown downward with the same initial speed?
3. At what height would the stone reach its maximum velocity?
4. How long would it take for the stone to reach a height of 2.0 meters?
5. What is the total distance traveled by the stone when it returns to the ground?

**Tip:** In problems involving vertical motion, remember that gravity always acts downward with a constant acceleration of \( 9.8 \, \text{m/s}^2 \), and it affects both the speed and height of an object.

A student throws a stone vertically up with a velocity of 7.0 m/s. What is the velocity of the stone at a height of 2.0 m above the starting position?

Learn how to calculate the velocity of a stone thrown upwards with an initial velocity of 7.0 m/s when it reaches a height of 2.0 m. The solution involves the kinematic equation v^2 = u^2 - 2gh and is suitable for high school students (Grades 9-12).

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