Use the following information for the remaining multiple-choice questions: When

Question

Use the following information for the remaining multiple-choice questions: When an object with mass m is dropped near the surface of Earth, it will fall to the ground due to the force of gravity. Near the surface the force of gravity, F, can be determined from the following equation: F = m g where g is the acceleration due to gravity (g = 9.8 m/s2 ). In the presence of air, a falling object will also experience an air resistance, Fa, which opposes the motion of the object. The net force on an object with mass m falling through the air near the surface of Earth is thus given by: Fnet = m g - Fa The air resistance, Fa, depends on such factors as the speed, size, shape, and surface texture of the object.

18. In another experiment, the scientist drops an object from a high-flying balloon. The object reaches terminal velocity after 8 seconds. During which time interval does it travel the greatest distance? A) 0-1s B) 2-3 s C) 4-5 s D) 6-7 s

Explanation / Answer

Intutively it's acceleration is decresing as time passes but to be precise;

It will traverse maximum distance in 0-1 s interval as under drag force application ;

Fnet = Fa + mg

anf Fnet = Kv where v is particles's speed at that instant

this gives second order equation whose solution provides velocity equal to (constant *(1-e^(-t))

whose integration in 0-1 s gives maximum

as from above => Distance = 1+(some constant) * (e^(T1)-e^(T2))

where T1 T2, are time instances like 0and 1 ; 1and 2 and so on

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