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An object of mass 10 kg is released from rest 4000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 40 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m/sec² and let x(t) represent the distance the object has fallen in t seconds.

An object of mass 10 kg is released from rest 4000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 40 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m/sec² and let x(t) represent the distance the object has fallen in t seconds.

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An object of mass 10 kg is released from rest 4000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 40 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m/sec² and let x(t) represent the distance the object has fallen in t seconds. Determine the equation of motion of the object. x(t) = When will the object hit the ground? The object will hit the ground after seconds. (Round to two decimal places as needed.)
Transcribed Image Text:An object of mass 10 kg is released from rest 4000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 40 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m/sec² and let x(t) represent the distance the object has fallen in t seconds. Determine the equation of motion of the object. x(t) = When will the object hit the ground? The object will hit the ground after seconds. (Round to two decimal places as needed.)
A parachutist whose mass is 85 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 = 90 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 20 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.
Transcribed Image Text:A parachutist whose mass is 85 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 = 90 N-sec/m when the chute is open. If the chute does not open until the velocity of the parachutist reaches 20 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.
Expert Solution
Step 1

"Since you have asked multiple questions, I am answering first question as per Bartleby guidelines."

Given,

Mass of the object = 10 kg =m

The object released from height, h = 4000 m

Proportionality constant, b = 40 N sec/m

Acceleration due to gravity = 9.81 m/s2

Assume initial velocity, V0 = 0 m/s

The gravitational force acts downwards and the air resistance acts upwards. Therefore, from Newton's second laws of motion,

m dv(t)dt = mg - b v(t)

dv(t)dt = g - bmv(t)

 

 

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