The formula v equals the square root of the quantity 64 multiplied by h end of quantity gives the velocity v in feet per second of an object that has fallen h feet. find the velocity of an object that has fallen 84 feet. round to the nearest hundredth.

a. 51.85 ft/sec

b. 5376 ft/sec

c. 12.96 ft/sec

d. 73.32 ft/sec

The equation is derived from the conservation of energy, specifically from potential energy stored at a given height in a gravitational field.

When potential energy is completely converted to kinetic energy you have:

(mv^2)/2=mgh  divide both sides by the mass m

v^2/2=gh  multiply both sides by 2

v^2=2gh take the square root of both sides

v=√(2gh)  and working with imperial units for acceleration due to gravity, g=-32ft/s^2

v=√(-64h)  but the change of h as it falls is negative h so

v=-√(64h) so if an object falls from a height of 88ft we have:

v=-√(64*84)

v=-√5376

v≈-73.32 ft/sec (to the nearest hundredth of a foot per second)

Note that this is the velocity, it is negative 73.32 ft/sec.

The question inadvertently asked for velocity and provided answers for SPEED.  Velocity is a vector and has both magnitude and direction, whereas speed just has magnitude.

So its final speed is 73.32 ft/sec

So if they actually wanted velocity none of their answers is correct :P

Welp life just is hard