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. 

Δd=vi t+12gt2



How long should it take the watermelon to hit the ground?
A.1.03 s

B.2.28 s

C.3.13 s

D.9.8 s


To solve this problem, we can use the kinematic equation provided:

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

Here:
- \(\Delta d\) is the displacement (5.20 m, the height of the bleachers),
- \(v_i\) is the initial velocity (since the watermelon is dropped, \(v_i = 0\)),
- \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\)),
- \(t\) is the time we want to find.

Since the initial velocity \(v_i = 0\), the equation simplifies to:

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

Substitute the known values:

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

Simplify the equation:

\[
5.20 = 4.9 t^2
\]

Solve for \(t^2\):

\[
t^2 = \frac{5.20}{4.9} = 1.0612
\]

Now, take the square root of both sides to solve for \(t\):

\[
t = \sqrt{1.0612} \approx 1.03 \, \text{seconds}
\]

Thus, the time it takes for the watermelon to hit the ground is approximately **1.03 seconds**, so the correct answer is:

**A. 1.03 s**

---

Would you like more details or have any questions? Here are some related questions to expand on this:

1. How would the time change if the height of the bleachers doubled?
2. What would happen if the watermelon were thrown downwards with an initial velocity?
3. How does the acceleration due to gravity influence the motion of falling objects?
4. If air resistance were significant, how would that affect the result?
5. What is the difference between free fall and projectile motion?

**Tip**: In free fall, the only force acting on the object is gravity, and the initial velocity is often zero unless the object is thrown.

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? A. 1.03 s, B. 2.28 s, C. 3.13 s, D. 9.8 s

Calculate the time it takes for a watermelon to hit the ground after being dropped from a height of 5.20 meters using the kinematic equation Δd = (1/2) g t^2. Learn the step-by-step process of solving for time, considering gravity and initial velocity. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation