3) Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that dv/dt=-kv2. It is known that a body’s initial velocity of v0 is observed at location x0. a. Estimate the body’s velocity and the position at any time t>0 correctly. b. Comment on the difference between this type of medium and the one in Number 1. PS: Please answer number 3 only and that number 1 is only for reference to make a difference.
1) Suppose that a body moves through a resisting medium with resistance
proportional to its velocity v, so that dv/dt=-kv. It is known that a body’s initial velocity of v0 is observed at location x0.
a. Estimate the body’s velocity and the position at any time t>0 correctly.
b. Conclude that the body travels only a finite distance and determine that
distance correctly.
3) Suppose that a body moves through a resisting medium with resistance
proportional to its velocity v, so that dv/dt=-kv2. It is known that a body’s initial velocity of v0 is observed at location x0.
a. Estimate the body’s velocity and the position at any time t>0 correctly.
b. Comment on the difference between this type of medium and the one in
Number 1.
PS: Please answer number 3 only and that number 1 is only for reference to make a difference.
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