Question

0. The weight of an object on the Moon is about 16.5% of its weight on Earth. The weight of an astronaut on the Moon is 24.75 pounds. How much does the astronaut weigh on Earth?

Answer 1

The astronaut weighs approximately 150 pounds on Earth, calculated by dividing their weight on the Moon (24.75 pounds) by 0.165, the fraction representing the Moon's gravity compared to Earth.

Step-by-step explanation:

To calculate the weight of an astronaut on Earth based on their weight on the Moon, we use the fact that the Moon's gravity is about 16.5% of the Earth's gravity. If the astronaut's weight on the Moon is 24.75 pounds, we can set up a simple proportion where 16.5% (or 0.165) of the Earth weight (WEarth) is equal to the Moon weight (WMoon). So, 0.165 × WEarth = WMoon.

To find the astronaut's weight on Earth (WEarth), we divide the Moon weight by 0.165:

WEarth = WMoon / 0.165 = 24.75 pounds / 0.165 ≈ 150 pounds

Hence, the astronaut weighs approximately 150 pounds on Earth. It's worth noting that mass is constant between Earth and the Moon, but weight changes because of the difference in gravity. The gravity on the Moon is about 1.625 m/s², while on Earth it is 9.80 m/s².

Answer 2

Answer: 150 pounds

Step-by-step explanation:

Let the the astronaut weight on Earth be represented by x.

Based on the information given in the question, thus can be formed into an equation as:

16.5% of x = 24.75

16.5% × x = 24.75

16.5/100 × x = 24.75

0.165x = 24.75

x = 24.75/0.165

x = 150 pounds

The astronaut weigh 150 pounds on Earth.