Question

2. The falling object satisfies the initial value problem dv/dt = 9. 8 - (v/2) at...

2. The falling object satisfies the initial value problem dv/dt = 9. 8 - (v/2) at v(0) = 0.

a. Find the time that must be elapsed for the object to reach 95% of its limiting velocity?

b. How far does the object fall during this time?

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Answer #1

Given:

  at v(0) = 0

a) The given equation can be written as

Integrating both side:

The maximum value of the velocity is .

The value of .

When, v = 95% of maximum velocity, the time elapsed is

[answer]

b) We will use this to find distance covered in time t = 6.0 s.

[answer]

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