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

Answer:

$kgkm^{-2}hr^{-1}$

Step-by-step 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 $\dfrac{df(10,t)}{dt}$

Since $V=f(d, t), \dfrac{df(10,t)}{dt}=\dfrac{dV}{dt}$

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