Question

The fallout V from a volcanic explosion (measured in kilograms per square kilometer) depends on the distance d from the volcano and the time t since the explosion began, so V equals f (d comma t ). Time is measured in hours and distance is measured in kilometers. What are the units of fraction numerator d f (10 comma t )over denominator d t end fraction?

Answer 1

`kgkm^(-2)hr^(-1)`

Explanation:

V=f(d, t) (measured in kilograms per square kilometer)

Time, t is measured in hours

Distance, d is measures in Kilometers

We want to determine the unit of
`(df(10,t))/(dt)`

Since
`V=f(d, t), (df(10,t))/(dt)=(dV)/(dt)`

`Unit \:of\: V=f(d, t)=kg/km^2\\\text{Unit of t}=hr\\\text{Therefore the Unit of } (dV)/(dt)=(kg/km^2)/(hr) \\=(kg)/(km^2hr) \\\\=kgkm^(-2)hr^(-1)`