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Sagot :
Answer:42.336 pounds
Step-by-step explanation:
To determine how much the bowling ball weighs on Earth given that it weighs 16 pounds on Mars, we need to understand the relationship between the weights on different planets.
The weight of an object depends on the gravitational acceleration at the surface of the planet. On Earth, the gravitational acceleration is approximately \( g_E = 9.81 \) meters per second squared (m/s²), while on Mars it is \( g_M = 3.71 \) m/s².
The weight \( W \) of an object is given by the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the object and \( g \) is the gravitational acceleration.
Let's denote the weight of the bowling ball on Earth as \( W_E \) and on Mars as \( W_M \).
Given:
\[ W_M = 16 \text{ pounds} \]
Now, to find \( W_E \):
\[ W_E = W_M \cdot \frac{g_E}{g_M} \]
Substitute the values:
\[ W_E = 16 \text{ pounds} \cdot \frac{9.81 \text{ m/s}^2}{3.71 \text{ m/s}^2} \]
Calculate the ratio:
\[ \frac{9.81}{3.71} \approx 2.646 \]
Now multiply by 16 pounds:
\[ W_E \approx 16 \cdot 2.646 \]
\[ W_E \approx 42.336 \text{ pounds} \]
Therefore, the bowling ball weighs approximately \( \boxed{42.336} \) pounds on Earth.
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