Question

b) The volume of an object as a function of time is calculated by 

V= At³ + B/t, where t is time measured in seconds and V is in cubic meters. Determine the dimension of the constants A and B.                           

c. A vector B, when added to the vector C = 3.0i+4.0j, yields a resultant vector that is in the positive y-direction and has a magnitude equal to that of C. What is the magnitude of B? 

Answer 1

b)

[A]=L^3T^{-3}\\ [B]=L^3T

c)

$$C=\sqrt{3^2+4^2}=5\\B_x=-3\\B_y+4=5\\B_y=1\\B=\sqrt{(-3)^2+1^2}=\sqrt{10}$$