H

We can determine the height of the building using the kinematic equations of motion. Here's how we approach the problem step by step:

Given:

• You observe the watermelon at a height of 30.0 m above the ground.
• The time between seeing the watermelon and it hitting the ground is $t = 1.50 \, \text{s}$.
• The acceleration due to gravity $g = 9.80 \, \text{m/s}^2$ (since air resistance is neglected).
• The initial velocity $v_0 = 0 \, \text{m/s}$ (since the watermelon was dropped).

We can first find the velocity of the watermelon after 1.50 s when it hits the ground, then calculate the height from which it was dropped.

Step 1: Using the kinematic equation to find the total height the watermelon fell from the point you spotted it (30.0 m above the ground):

$h = v_0 t + \frac{1}{2} g t^2$ Since the watermelon is falling from rest, $v_0 = 0$, so the equation simplifies to: $h = \frac{1}{2} g t^2$

Substituting the values: $h = \frac{1}{2} (9.80 \, \text{m/s}^2)(1.50 \, \text{s})^2$

Let’s calculate the distance $h$.The watermelon falls a distance of $11.025 \, \text{m}$ during the 1.50 seconds.

Step 2: Total height of the building

Since the watermelon was 30.0 m above the ground when you first saw it and then fell an additional 11.025 m, the total height of the building is:

$H = 30.0 \, \text{m} + 11.025 \, \text{m} = 41.025 \, \text{m}$

Thus, the height of the building is approximately $41.0 \, \text{m}$.

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Would you like further details or explanations on any part of this? Here are some related questions to consider:

1. What is the velocity of the watermelon when it hits the ground?
2. How much time did the watermelon take to fall the entire distance from the building?
3. What if air resistance was not neglected? How would the motion change?
4. How would the result change if the building was on a hill with a sloped ground?
5. Can we use energy conservation principles to solve this problem?

Tip: When solving free-fall problems, always start by identifying whether the object was dropped or thrown, as this affects the initial velocity.