A diver runs horizontally with a speed of 1.30 m/s off a platform that is 8.6 m above the water. What is his speed just before striking the water?

8.6 = 4.9 t^2

t = 1.32 seconds to fall 8.6 meters
v = g t = 9.81*1.32 = 13 m/s
so
speed = sqrt (169 + 1.3*2) =sqrt(169+1.69)
=13.06 m/s

To determine the speed of the diver just before striking the water, we can use the principle of conservation of energy. At the platform, the diver possesses potential energy due to his height above the water. Upon reaching the water, this potential energy is converted to kinetic energy.

The potential energy (PE) of an object is given by the formula:
PE = m*g*h

Where m is the mass of the object (which we don't have in this case), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the object above the reference point (8.6 m).

Since we're only interested in the speed of the diver, we don't need to know the mass. The kinetic energy (KE) is given by the formula:
KE = 1/2 * m * v^2

Where v is the speed of the diver.

According to the law of conservation of energy, the potential energy at the start (PE_start) is equal to the kinetic energy at the end (KE_end) of the motion:
PE_start = KE_end

Substituting the respective formulas and rearranging the equation, we get:
m * g * h = 1/2 * m * v^2

The mass of the diver (m) cancels out from both sides of the equation. Thus, the mass does not affect the final result.

Simplifying the equation further, we find:
g * h = 1/2 * v^2

Rearranging the equation to solve for v, we get:
v = √(2 * g * h)

Substituting the given values:
v = √(2 * 9.8 m/s^2 * 8.6 m)

Calculating this expression yields:
v ≈ √(168.28) ≈ 12.99 m/s

Therefore, the diver's speed just before striking the water is approximately 12.99 m/s.

To find the diver's speed just before striking the water, we can use the principle of conservation of energy. The initial potential energy of the diver at the top of the platform is converted into both kinetic energy and potential energy as the diver falls.

The initial potential energy can be calculated using the equation:

Potential energy = mass x gravity x height

Since the height of the platform is given as 8.6 m, we can use the approximate value for the acceleration due to gravity, 9.8 m/s^2, to calculate the initial potential energy.

Next, we equate this potential energy to the sum of kinetic energy and potential energy just before striking the water. At this point, the only potential energy remaining is due to the height of the diver above the water.

Finally, we solve for the final kinetic energy of the diver just before striking the water, and then find the corresponding speed using the equation:

Kinetic energy = 0.5 x mass x speed^2

Let's calculate the speed just before the diver strikes the water:

1. Calculate initial potential energy:
Potential energy = mass x gravity x height

2. Calculate the final potential energy just before striking the water:
Potential energy = mass x gravity x water_height

3. Equate the initial potential energy to the sum of final potential energy and final kinetic energy:
Initial potential energy = final potential energy + final kinetic energy

4. Solve for the final kinetic energy:
Final kinetic energy = Initial potential energy - final potential energy

5. Solve for the speed just before striking the water using the equation for kinetic energy:
Final kinetic energy = 0.5 x mass x speed^2

6. Rearrange the equation and solve for speed:
speed = √(2 x Final kinetic energy / mass)

By following these steps, you should be able to calculate the diver's speed just before striking the water.