Neglecting air resistance and the weight of the propellant, determine the work (mi-tons) done in propelling a four-metric-ton satellite to a height of 220 miles above Earth. (Use 4,000 miles as the radius of Earth. Round your answer to two decimal places.)

the work done in propelling the satellite is 919.2 mile-tons

Step-by-step explanation:

Given the data in the question;

we know that, the weight of a body varies inversely as the square of its distance from center of of earth;

⇒ F(x) = c / x²

given that F(x) = four-metric-ton = 4 × 1.102 = 4.408 tons

radius of earth = 4000 miles

we substitute

⇒ 4.408 = c / ( 4000 )²

c = 4.408 × ( 4000 )² = 70528000

so increment of work will be;

ΔW = ( 70528000 / x² ) Δx

Now work done in propelling to a height of 220 miles above Earth;

W = ₄₀₀₀∫⁴²²⁰  ( 70528000 / x² ) dx

W = 70528000[ - 1/x ]⁴²²⁰₄₀₀₀

W = 70528000[ - 1/4220 + 1/4000 ]

W = 70528000[ 1.3033175 × 10⁻⁵ ]

W = 919.2 mile-tons

Therefore, the work done in propelling the satellite is 919.2 mile-tons

146%

step-by-step explanation: