We can use the law of conservation of mechanical energy to find the speed or the height of a falling object just before it hits the ground by using the formula:
KE + PE = constant
Where KE is the kinetic energy and PE is the potential energy. The kinetic energy of an object is given by the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity. The potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
Since the total mechanical energy of the object is conserved, we can set the initial mechanical energy equal to the final mechanical energy and solve for the unknown variable. For example, if we want to find the speed of the object just before it hits the ground, we can set the initial potential energy equal to the final kinetic energy and solve for the velocity:
mgh = 1/2mv^2
v = sqrt(2gh)
Similarly, if we want to find the height of the object just before it hits the ground, we can set the initial kinetic energy equal to the final potential energy and solve for the height:
1/2mv^2 = mgh
h = v^2/(2g)
By using the law of conservation of mechanical energy and the formulas for kinetic and potential energy, we can find the speed or the height of a falling object just before it hits the ground.