Make the base of the building zero. Then the initial distance is 100m, final distance unknown x. Use gravity, time and initial velocity to solve for final distance.
x - 100 = (0)(5) +(1/2)(-9.81)(5^2)
x - 100 = 0 - 122.625
x = -122.625 + 100
x = -22.625 m below ground
Answer:
0.853 m/s
Explanation:
Total energy stored in the spring = Total kinetic energy of the masses.
1/2ke² = 1/2m'v².................... Equation 1
Where k = spring constant of the spring, e = extension, m' = total mass, v = speed of the masses.
make v the subject of the equation,
v = e[√(k/m')].................... Equation 2
Given: e = 39 cm = 0.39 m, m' = 0.4+0.4 = 0.8 kg, k = 1.75 N/cm = 175 N/m.
Substitute into equation 2
v = 0.39[√(1.75/0.8)
v = 0.39[2.1875]
v = 0.853 m/s
Hence the speed of each mass = 0.853 m/s
Answer:
The rate of change of the area when the bottom of the ladder (denoted by
) is at 36 ft. from the wall is the following:

Explanation:
The Area of the triangle is given by
where
(by using the Pythagoras' Theorem) and
is the length of the base of the triangle or the distance between the bottom of the ladder and the wall.
The area is then

The rate of change of the area is given by its time derivative


Product rule
Chain rule


In here we can identify
,
and
.
The result is then
