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 m5.20 m above the ground.

Δd=vi t+12gt2Δd=vi t+12gt2

How long should it take the watermelon to hit the ground?

We can determine how long it will take for the watermelon to hit the ground by using the equation of motion:

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

Where:
- \(\Delta d\) is the displacement (in this case, 5.20 m),
- \(v_i\) is the initial velocity (which is 0 m/s because the watermelon is dropped from rest),
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(t\) is the time we are solving for.

Since the watermelon is dropped from rest, \(v_i = 0\), and the equation simplifies to:

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

Substituting the values:

\[
5.20 = \frac{1}{2} \times 9.81 \times t^2
\]

Now we solve for \(t\):

\[
5.20 = 4.905 t^2
\]

\[
t^2 = \frac{5.20}{4.905} \approx 1.06
\]

\[
t \approx \sqrt{1.06} \approx 1.03 \, \text{seconds}
\]

Thus, it should take approximately **1.03 seconds** for the watermelon to hit the ground.

Would you like further details on any step or have questions? Here are 5 related questions:

1. How would the time change if the height was doubled?
2. How would air resistance affect this calculation?
3. What is the final velocity of the watermelon just before hitting the ground?
4. What would happen if the initial velocity was not zero?
5. How can you calculate the impact force on the watermelon?

**Tip**: The formula used here assumes no air resistance. In real-world conditions, factors like air drag might slightly alter the result.

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. How long should it take the watermelon to hit the ground?

Determine how long it takes for a watermelon dropped from a height of 5.20 m to hit the ground. This problem covers kinematic equations and is suitable for students in Grades 9-12. Learn the step-by-step process using the equation Δd = (1/2) * g * t^2 to calculate the time of free fall.

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