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This problem describes a scenario where a watermelon is dropped from a height of 5.20 meters. The goal is to determine information about its free fall, such as the time taken for it to reach the ground, using the given formula for displacement in free fall:

\[
\Delta d = v_i t + \frac{1}{2} g t^2
\]

where:
- \(\Delta d = -5.20 \, \text{m}\) (displacement, negative because it's falling downward),
- \(v_i = 0 \, \text{m/s}\) (initial velocity, since the watermelon is dropped from rest),
- \(g = 9.8 \, \text{m/s}^2\) (acceleration due to gravity),
- \(t\) is the time it takes for the watermelon to hit the ground.

Since the initial velocity is zero, the equation simplifies to:

\[
\Delta d = \frac{1}{2} g t^2
\]

Now, solving for \(t\):

\[
-5.20 = \frac{1}{2} (9.8) t^2
\]

Let's compute the time \(t\).The time it takes for the watermelon to reach the ground is approximately **1.03 seconds**.

Would you like more details or have any questions about this process? Here are some related questions to expand your understanding:

1. How would the time change if the watermelon was thrown downward with an initial velocity?
2. What is the velocity of the watermelon just before it hits the ground?
3. How would the time be affected if the height was doubled?
4. How much time would it take if the object was dropped on the moon, where gravity is about 1.62 m/s²?
5. What other factors could influence the time it takes for the watermelon to hit the ground, such as air resistance?

**Tip:** In free fall problems, always check if the initial velocity is zero to simplify calculations.

Your physics teacher takes your class outdoors to a stand of bleachers. You climb to the top and drop a watermelon to the ground below. One of your classmates measures the height of the bleachers to be 5.20 m above the ground. Calculate the time taken for the watermelon to hit the ground.

Calculate the time it takes for a watermelon to hit the ground when dropped from a height of 5.20 meters. The problem explores key physics concepts such as free fall, kinematics, and gravitational acceleration. Ideal for high school students (Grades 9-12).

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