Question

A rocket developed by an amateur was traveling upwards at a velocity given by v = (11 + 0.2s) m/s, where s is in meters. Determine the time for the rocket to reach an altitude of s = 80 m. Initially, s = 0 when t = 0. [Hint: obtain initial velocity].

Answer 1

Time taken to reach 80 meters equals 4.4897 seconds.

Step-by-step explanation:

We know that velocity is related to position as

`v=(ds)/(dt)`

Now it is given that
`v=(11+0.2v`

Using the given velocity function in the above relation we get

`(ds)/(dt)=(11+0.2s)\\\\(ds)/((11+0.2s))=dt\\\\\int (ds)/((11+0.2s))=\int dt\\\\`

Now since the limits are given as

1) at t = 0 , s=0

Using the given limits we get

`\int_(0)^(80) (ds)/((11+0.2s))=\int_(o)^(t) dt\\\\(1)/(0.2)[ln(11+0.2s)]_(0)^(80)=(t-0)\\\\5* (ln(11+0.2* 80)-ln(11))=t\\\\\therefore t=4.4897seconds`