Atrain at a constant 79.0 km/h moves east for 27.0 min, then in a direction 50.0° east of due north for 29.0 min, and then west for 37.0 min. what are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip?

Magnitude of avg velocity,

Given:

Constant speed of train, v = 79 km/h

Time taken in East direction, t = 27 min =

Angle,

Time taken in east of due North direction, t' = 29 min =  

Time taken in west direction, t'' = 37 min =  

Solution:

Now, the displacement, 's' in east direction is given by:

Displacement in   east of due North for 29.0 min is given by:

Now, displacement in the west direction for 37 min:

Now, the overall displacement,

(a) Now, average velocity, is given:

Magnitude of avg velocity is given by:

(b) angle can be calculated as:

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =