The weight (V) of an object on Venus varies directly as its weight (E) on Earth. A person weighing 120 lb on Earth would weigh 106 lb on Venus. How much would a person weighing 180 lb on Earth weigh on Venus?
V = kE
106 = k*120
k = 53/60
53/60 * 180 = 159
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To solve this problem, we can set up a proportion between the weights on Earth and Venus:
Venus weight / Earth weight = Venus gravitational constant / Earth gravitational constant
Let's denote the weight on Earth as E1, the weight on Venus as V1, and the weight given as E2 (180 lb). We can plug in the values we have into the proportion:
V1 / E2 = V / E1
Using the information provided, we know that V1 (weight on Venus for a person weighing 120 lb on Earth) is 106 lb, and E1 (weight on Earth for a person weighing 120 lb) is 120 lb. Now we can solve for V:
106 lb / 180 lb = V / 120 lb
Cross multiplying:
106 lb * 120 lb = V * 180 lb
Dividing both sides by 180 lb:
(106 lb * 120 lb) / 180 lb = V
Simplifying:
70.6667 = V
Therefore, a person weighing 180 lb on Earth would weigh approximately 70.67 lb on Venus.
To find out how much a person weighing 180 lb on Earth would weigh on Venus, we can set up a proportion using the given information.
Let's assume the weight on Earth is represented as E, and the weight on Venus is represented as V.
According to the given information, the weight on Venus (V) varies directly with the weight on Earth (E). This means we can set up the proportion:
V/E = k
Where k is the constant of variation.
From the problem, we are given that a person weighing 120 lb on Earth would weigh 106 lb on Venus. Setting up the proportion using this information, we get:
106/120 = k
Simplifying, we find that k = 0.8833 (rounded to four decimal places).
Now, we can use this value of k to find the weight on Venus for a person weighing 180 lb on Earth.
V/E = k
V/180 = 0.8833
Cross multiplying, we get:
V = 180 * 0.8833
Calculating this, we find that V ≈ 159 lb.
Therefore, a person weighing 180 lb on Earth would weigh approximately 159 lb on Venus.