Due : November 13 The weight of any object decreases as the distance from Earth\

Question

Due : November 13 The weight of any object decreases as the distance from Earth's surface increases. As the object rises, the effect of Earth's gravitational pull on the object is reduced. The weightlessness that astronauts experience in the space shuttle as it orbits Earth is partially due to the distance that the shuttle is above Earth's surface If an object weighs E kilograms at sea level on Earth's surface, then the weight W'of the object at a distance of h kilometers above sea level is given by the function: 6400 Suppose you are flying in a commercial jet liner 15 kilometers above sea level. Replace E with 65 kilograms and calculate the body weight at 15 km above sea level. 1. 2. If an astronaut weighs 70 kg at sea level write a function that expresses the astronaut's weight as a function of his/her distance from sea level. 3. Complete the following table using the equation from Part 2. h0 10 100 100015002000 10,000 20,000

Explanation / Answer

Answer (1)

The equation for weight with respect to the height is given as below

W(h) =   E / [(1) + (h/6400)] 2

Here,

·       W(h) is the Weight of the object at height h = This is to be calculate in this question.

·       E is the weight of the object at sea level = 65 kg

·       h is the height of the object from sea level = 15 km

W(h) =   65 / [(1) + (15/6400)] 2

W(h) =   65 / [(1) + 0.002344] 2

W(h) =   65 / [(1.002344] 2

W(h) =   65 / 1.004693

W(h) =   64.69638 kg   

W(15) =   64.69638 kg     - The weight of the object reduced from 65 kg at sea level to 64.69638 kg at a height of 15 km above the sea level.

Answer (2)

The equation for weight with respect to the height is given as below

W(h) =   E / [(1) + (h/6400)] 2

Here,

·       W(h) is the Weight of the astronaut at height h.

·       E is the weight of the astronaut at sea level = 70 kg

·       h is the height of the object from sea level.

W(h) =   70 / [(1) + (h/6400)] 2

This equation gives the weight of the astronaut with respect to the height from seal level.

Answer (3) - Using the above equation with E = 70 kg and H as per the table value, we have W(h) as below

h 0 10 100 1000 1500 2000 10000 20000 W(h) 70 69.78 67.86 52.36 45.94 40.63 10.66 4.11

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