A diver runs horizontally off the end of a diving board with an initial speed of 1.25 m/s. If the diving board is 3.20 m above the water, what is the diver's speed just before she enters the water? (Neglect air resistance.)
To solve this problem, we can use the principle of conservation of energy. At the initial position on the diving board, the diver has only potential energy, which gets converted into kinetic energy as the diver falls towards the water.
First, let's calculate the potential energy of the diver at the initial position:
Potential Energy (PE) = mass (m) * gravity (g) * height (h)
Since the diver's mass is not given in the question, we can ignore it because it cancels out when we compare the initial and final energies.
PE = m * g * h
where g is the acceleration due to gravity (9.8 m/s²) and h is the height of the diving board (3.20 m).
PE = 9.8 m/s² * 3.20 m
PE = 31.36 J
This potential energy (PE) gets converted into kinetic energy (KE) just before the diver enters the water. The equation for kinetic energy is:
Kinetic Energy (KE) = (1/2) * mass (m) * velocity^2
However, we are only interested in the speed just before entering the water, which is the magnitude of the velocity. So, we can rewrite the equation without the mass:
KE = (1/2) * velocity^2
At the initial position, all the potential energy gets converted into kinetic energy, so:
PE = KE
31.36 J = (1/2) * velocity^2
Now, let's solve for the velocity:
31.36 J = (1/2) * velocity^2
Divide both sides by (1/2):
62.72 J = velocity^2
Take the square root of both sides:
velocity = √62.72 J
velocity ≈ 7.92 m/s
Therefore, the diver's speed just before entering the water is approximately 7.92 m/s.
To solve this problem, we can use the principle of conservation of energy.
First, let's find the potential energy of the diver at the initial position on the diving board. The potential energy is given by the formula:
Potential energy = mass × gravity × height
Since the mass of the diver is not given, we can ignore it because we are only interested in finding the speed of the diver. The value of gravity is approximately 9.8 m/s^2, and the height is 3.20 m. Therefore, the potential energy at the start is:
Potential energy = 9.8 m/s^2 × 3.20 m = 31.36 J
Now, let's find the kinetic energy of the diver just before entering the water. The kinetic energy is given by the formula:
Kinetic energy = 1/2 × mass × velocity^2
Again, we can ignore the mass since we are only interested in the velocity. Therefore, the kinetic energy is simply:
Kinetic energy = 1/2 × velocity^2
According to the principle of conservation of energy, the total energy at the start (potential energy) is equal to the total energy just before entering the water (kinetic energy). Therefore,
31.36 J = 1/2 × velocity^2
Now, let's solve for the velocity. We can rearrange the equation:
velocity^2 = 2 * 31.36 J
velocity^2 = 62.72 J
velocity = √(62.72 J)
Using a calculator, we find that the velocity is approximately 7.92 m/s.
So, the diver's speed just before entering the water is approximately 7.92 m/s.
find the time it takes to fall 3.2m
3.2=1/2 g t^2
then, take that time and find the distance moved horizntally.
d=1.25*t