Question

1 (KE, PE) An object of mass 90 lbm is projected straight upward from the surface of the earth and reaches a height of 900 ft when its velocity reaches zero. The only force acting on the object is the force of gravity. The acceleraton of gravity is g = 32.2 ft/s2 . Determine the initial kinetic energy of the object [ft·lbf], and the object’s initial velocity [ft/s].

Answer 1

To determine the initial kinetic energy of the object, subtract its potential energy from the total mechanical energy. The initial velocity can be calculated using the equation v² = u² + 2as.

Step-by-step explanation:

To determine the initial kinetic energy of the object, we need to consider the conservation of mechanical energy. The mechanical energy (E) of the object is the sum of its kinetic energy (KE) and potential energy (PE). Since the object reaches a height of 900 ft, its potential energy at that height is PE = mgh = (90 lbm)(32.2 ft/s²)(900 ft). Therefore, the initial kinetic energy can be found by subtracting the potential energy from the total mechanical energy: KE = E - PE.

As for the object's initial velocity, it can be calculated using the equation v² = u² + 2as, where v = 0 ft/s (velocity at the highest point), u is the initial velocity, a is the acceleration (g = 32.2 ft/s²), and s is the displacement (900 ft). Rearranging the equation, we get u = sqrt(v² - 2as).