Question

A 1 kilogram metallic object falls from a height of 50 meters and air resistance assumed...

A 1 kilogram metallic object falls from a height of 50 meters and air resistance assumed negligible formulate the mathematical model. If it’s initial height is 20 meters, how long will it take for the object to reach the ground? apply it using differential equations.

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Homework Answers

Answer #1

For a body falling to ground, the force on it is only gravitational force due to earth.

Therefore, by Newton's law

g is acceleration due to gravity.

Therefore

g is constant for near the surface of earth

Taking integration

Therefore

vf is velocity at time t

vu is velocity at time t=0

The above equation can be written as

Taking integration gain

s is displacement

Therefore

For s=20, and initial velocity is zero

g=10

Therefore,

t=2 seconds

Therefore, it takes 2 seconds to reach ground from a height s=20metres

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