Answer:
See below
Step-by-step explanation:
Write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height.
if v(t) is the speed at time t after being dropped, v'(t) is the acceleration at time t, so the the initial value problem for the downward velocity is
v'(t) = 10 - 0.1v(t)
v(0) = 0 (since the object is dropped)
<em> The equation v'(t)+0.1v(t)=10 is an ordinary first order differential equation with an integrating factor </em>
so its general solution is
To find C, we use the initial value v(0)=0, so C=-100
and the solution of the initial value problem is
what is the terminal velocity?
The terminal velocity is
How long before the object reaches 90% of terminal velocity?
90% of terminal velocity = 90 m/sec
we look for a t such that
How far has it fallen by that time?
The distance traveled after t seconds is given by
So, the distance traveled after 23.026 seconds is