Question

If a ball is dropped from a height its velocity will increase until it hits the ground, assuming that aerodynamic drag due to the air is negligible. During its fall, its initial potential energy is converted into kinetic energy. If the ball is dropped from a height of 800 centimeters [cm], and the impact velocity is 41 feet per second [ft/s], determine the value of gravity in units of meters per second squared [m/s2].

Answer 1

Answer:

g = 9.69 m/s²

Explanation:

given,

height from where ball is dropped = 800 cm = 8 m

impact velocity = 41 ft/s = 41 × 0.3048 = 12.45 m/s

acceleration due to gravity = ?    

initial potential energy is given by

PE = m g h                          

     = m g × 8                            

     = 8 mg..............(1)

now final kinetic energy

$KE= \dfrac{1}{2}m(v)^2$

$KE= \dfrac{1}{2}m(12.45)^2$

            =77.50 m.....................(2)

comparing equation (1) to (2)

8 mg = 77.50 m

g = 77.5/8

g = 9.69 m/s²