To determine the maximum height reached by a stone thrown vertically upward with an initial velocity, we can use the following kinematic equation:

$v^2 = u^2 + 2as$

where:

• $v$ is the final velocity (0 m/s at maximum height),
• $u$ is the initial velocity (35 m/s),
• $a$ is the acceleration due to gravity (−9.8 m/s², acting downward),
• $s$ is the maximum height reached.

Step-by-Step Solution

1. Set up the equation with $v = 0$: $0 = (35)^2 + 2 \times (-9.8) \times s$

2. Solve for $s$: $0 = 1225 - 19.6s$ $19.6s = 1225$ $s = \frac{1225}{19.6}$ $s \approx 62.5 \text{ meters}$

Answer

The maximum height reached by the stone is approximately 62.5 meters.

Would you like more details on this calculation or have any further questions?

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1. What would the time to reach the maximum height be?
2. How would the maximum height change if the initial speed were doubled?
3. What would the total time of flight be until the stone returns to the initial point?
4. How would air resistance affect the maximum height in a real-world scenario?
5. How can we calculate the velocity at various points before reaching the maximum height?

Tip: When analyzing upward motion under gravity, the velocity will always be zero at the peak height before it begins to fall back down.