Task 1: Dimensional Analysis Part 1: Show that potential energy (mgh) is dimensionally the same as kinetic energy (1 mv). Show all your steps and work. In other words, show each side of the equation in its fundamental dimensions (they should be the same). mgh mv m is the mass g is acceleration due to gravity h is the height of the dropped object v is the velocity Part 2: Use this relationship to find the (max) velocity of an object if dropped from a height of 20. ft here on earth (where g = 9.8 m/s or 32.2 ft/s). Hint, plug in values and use algebra to solve for v. Give your answer in miles per hour. Task 2: Unit Conversion 1. 73.7 miles mm year sec Round answer to nearest hundredth. 2. 0.045 cal -kg rad ft lb. slug Write in scientific notation with 3 digits of precision. deg