A parachutist whose mass is 75 kg drops from a helicopter hovering 1500 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 30 N-sec/m when the chute is closed and b₂ = 100 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 15 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec².

A parachutist whose mass is 75 kg drops from a helicopter hovering 1500 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 30 N-sec/m when the chute is closed and b₂ = 100 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 15 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec².

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University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter6: Applications Of Newton's Laws

Section: Chapter Questions

Problem 40P: A service elevator takes a load of garbage, mass 10.0 kg, from a floor of a skyscraper under...

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Newton's Second Law

Newton’s laws of motion describe the relationship between the motion of an object and forces acting on it. Newton’s law of motion has two types as follows:

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A parachutist whose mass is 75 kg drops from a helicopter hovering 1500 m above the ground and falls toward the ground under the influence of gravity. Assume that
the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b₁ = 30 N-sec/m when the chute is closed and b₂ = 100
N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 15 m/sec, after how many seconds will the parachutist reach
the ground? Assume that the acceleration due to gravity is 9.81 m/sec².
The parachutist will reach the ground after
(Round to two decimal places as needed.)
seconds.

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Step 1: Given that:

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Step 2: Determination of time taken to reach the velocity of 30 m/s when parachute is closed:

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Step 3: Calculation of distance traveled in t(1) sec:

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Step 4: Determination of terminal velocity when parachute is open:

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Step 5: Determination of time taken t(2) to reach the terminal velocity:

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Step 6: Calculation of time t(3) taken to cover rest of the distance

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Step 7: Calculation of total time:

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