A standard gold bar stored at Fort Knox, Kentucky, is 7.00 inches long, 3.63 inches wide, and 1.75 inches tall. Gold has a density of 19,300 kg/m3. What is the mass of such a gold bar?

14.1 kg

Explanation:

Given:

Length=7.00inches

Width=3.63 inches

Height=1.75 inches

density = 19,300 kg/m3.

We can convert the given parameters to metre for unit consistency

But we know 1 inches= 0.0254 metre

✓Then Length l=7.00inches

=7×0.0254 metre=0.1778m

✓Width w =3.63 inches

==3.63 ×0.0254 metre=0.092m

✓Height h =1.75 inches

=1.75 ×0.0254 metre=0.0445 m

But Mass= density × volume

Volume= Length× width×height

Mass= density× Length× width×height

= 19300kg/m³×0.1778×0.0922×0.0445

=14.1 kg

Therefore, the mass of the gold bar is 14.1 kg

c. magnitude and direction

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west