Given that "mass" multiply by constant “k” is equal to "energy" divided by “height”. Determine, by using dimensions of each, which physical quantity is
represented by “k”?

K must be an acceleration

Explanation:

Recall that unit of energy consists the following dimensions:

mass * length^2 / time^2

then if we have :  mass * K = energy / length

then the units of K can be obtained by replacing the units of energy by (mass * length^2 / time^2), and then dividing by units of mass:

K = (mass * length^2 / time^2)/ (length * mass)

where we cancel out units of mass, and one unit of length resulting in units of length divided units of time squared. and such are units of acceleration. Therefore K must be an acceleration.

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.

hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )