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Let's analyze the problem step-by-step.

### Part A:
You were asked how high the stone is 2 seconds after being thrown upward from a height of 675 feet with an initial velocity of 14 feet per second, and with gravitational acceleration of -32 feet per second squared. Your answer of **639 feet** was marked as correct.

### Part B:
To determine when the stone hits the ground, let's set up the equation of motion and solve for the time at which the stone reaches a height of 0 feet (ground level).

1. **Position equation** (height \( h \) as a function of time \( t \)):
   \[
   h(t) = h_0 + v_0 t + \frac{1}{2} a t^2
   \]
   where:
   - \( h_0 = 675 \) feet (initial height),
   - \( v_0 = 14 \) feet per second (initial upward velocity),
   - \( a = -32 \) feet per second squared (acceleration due to gravity).

2. Substitute the values:
   \[
   h(t) = 675 + 14t - 16t^2
   \]

3. Set \( h(t) = 0 \) to find when the stone reaches the ground:
   \[
   0 = 675 + 14t - 16t^2
   \]

4. Rearrange into a standard quadratic form:
   \[
   -16t^2 + 14t + 675 = 0
   \]

5. Use the quadratic formula to solve for \( t \):
   \[
   t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \( a = -16 \), \( b = 14 \), and \( c = 675 \).

6. Substitute the values:
   \[
   t = \frac{-14 \pm \sqrt{14^2 - 4 \cdot (-16) \cdot 675}}{2 \cdot (-16)}
   \]

7. Simplify to find the two possible times, and choose the positive one, as time cannot be negative.

Would you like a detailed solution for the calculation, or any further clarification on this method?

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### Related Questions to Explore:

1. How would the answer change if the stone was thrown downward instead of upward?
2. What if the initial speed was doubled? How would that impact the time to hit the ground?
3. How would air resistance affect the time it takes for the stone to hit the ground?
4. Can you derive the maximum height reached by the stone?
5. What would the impact speed be when the stone hits the ground?

#### Tip:
Always double-check if your initial height and velocity align with the given values to avoid calculation errors.

A stone is thrown straight up from the edge of a roof, 675 feet above the ground, at a speed of 14 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 2 seconds later? B. At what time does the stone hit the ground?

Solve a kinematics problem involving a stone thrown upward from a 675-foot high roof at 14 feet per second. Learn how to determine the stone's height after 2 seconds and when it hits the ground, using quadratic equations and gravitational acceleration.

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