An object mass m1 falls from a height of h1.
a. Write a formula for the velocity of the object just before it stikes the ground in terms of g,m1,and h1.
b. Write a formula for the velocity of the object at the half way point in terms of g,m1, and h1.
a. V^2 = Vo^2 + 2g*h1. Vo = 0.
b. V^2 = Vo^2 + 2g*0.5h1. Vo = 0.
a. The formula for the velocity of the object just before it strikes the ground is given by:
v1 = sqrt(2 * g * h1), where g is the acceleration due to gravity.
b. The formula for the velocity of the object at the halfway point is given by:
v2 = sqrt(g * h1), where g is the acceleration due to gravity and h1 is the height from which the object is dropped.
a. To determine the velocity of the object just before it hits the ground, we can use the principle of conservation of energy. The initial potential energy when the object is at height h1 is converted into kinetic energy as it falls. Assuming negligible air resistance, we can equate these two energies.
The potential energy (PE) of the object at height h1 is given by:
PE = m1 * g * h1
Here, m1 is the mass of the object and g is the acceleration due to gravity.
The kinetic energy (KE) of the object just before it hits the ground is equal to the potential energy at height h1:
KE = m1 * v1^2 / 2
Here, v1 is the velocity of the object just before it hits the ground.
Equating the potential energy and kinetic energy, we have:
m1 * g * h1 = m1 * v1^2 / 2
Therefore, the formula for the velocity of the object just before it strikes the ground is:
v1 = sqrt(2 * g * h1)
b. To determine the velocity of the object at the halfway point, we can use the concept of conservation of mechanical energy. At the halfway point, half of the potential energy has been converted into kinetic energy.
The potential energy (PE) of the object at the halfway point, h1/2, is given by:
PE = m1 * g * (h1/2)
The kinetic energy (KE) of the object at the halfway point is equal to the potential energy at h1/2:
KE = m1 * v2^2 / 2
Here, v2 is the velocity of the object at the halfway point.
Equating the potential energy and kinetic energy, we have:
m1 * g * (h1/2) = m1 * v2^2 / 2
Simplifying the equation gives:
v2 = sqrt(2 * g * (h1/2))
Therefore, the formula for the velocity of the object at the halfway point is:
v2 = sqrt(g * h1)