Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

The table shows information about four objects resting at the top of a hill.

| Object | Mass (kg) | Potential Energy (J) |
|--------|-----------|----------------------|
| W | 50 | 980 |
| X | 35 | 1,029 |
| Y | 62 | 1,519 |
| Z | 24 | 1,176 |

Which object is on the tallest hill?

A. W
B. X
C. Y
D. Z


Sagot :

Let's solve this problem step-by-step to determine which object is on the tallest hill.

Step 1: Understand the Potential Energy formula

The potential energy ([tex]\( PE \)[/tex]) of an object is given by the formula:
[tex]\[ PE = m \cdot g \cdot h \][/tex]
where,
- [tex]\( PE \)[/tex] is the potential energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the gravitational acceleration (approximated as [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the hill.

Step 2: Rearrange the formula to solve for height ([tex]\( h \)[/tex])

To find the height, we rearrange the formula:
[tex]\[ h = \frac{PE}{m \cdot g} \][/tex]

Step 3: Calculate the height for each object

Given:
1. Object W:
- Mass ([tex]\( m \)[/tex]) = 50 kg
- Potential energy ([tex]\( PE \)[/tex]) = 980 J
[tex]\[ h_W = \frac{980}{50 \cdot 9.8} = \frac{980}{490} \approx 2 \, \text{m} \][/tex]

2. Object X:
- Mass ([tex]\( m \)[/tex]) = 35 kg
- Potential energy ([tex]\( PE \)[/tex]) = 1,029 J
[tex]\[ h_X = \frac{1,029}{35 \cdot 9.8} = \frac{1,029}{343} \approx 3 \, \text{m} \][/tex]

3. Object Y:
- Mass ([tex]\( m \)[/tex]) = 62 kg
- Potential energy ([tex]\( PE \)[/tex]) = 1,519 J
[tex]\[ h_Y = \frac{1,519}{62 \cdot 9.8} = \frac{1,519}{607.6} \approx 2.5 \, \text{m} \][/tex]

4. Object Z:
- Mass ([tex]\( m \)[/tex]) = 24 kg
- Potential energy ([tex]\( PE \)[/tex]) = 1,176 J
[tex]\[ h_Z = \frac{1,176}{24 \cdot 9.8} = \frac{1,176}{235.2} \approx 5 \, \text{m} \][/tex]

Step 4: Compare the heights to determine which hill is tallest

The heights for each object are:
- [tex]\( h_W \approx 2 \, \text{m} \)[/tex]
- [tex]\( h_X \approx 3 \, \text{m} \)[/tex]
- [tex]\( h_Y \approx 2.5 \, \text{m} \)[/tex]
- [tex]\( h_Z \approx 5 \, \text{m} \)[/tex]

Comparing these heights, we find that [tex]\( h_Z \approx 5 \text{m} \)[/tex] is the tallest.

Conclusion:
The object on the tallest hill is object [tex]\( Z \)[/tex].

So, the answer is:
[tex]\[ \boxed{Z} \][/tex]