A bird is flying with a speed of 18.0 m/s over water when it accidently drops a 2.00 kg fish. If the altitude of the bird is 5.40 m and the friction is disreguarded,what is the speed of the fish when it hits the water?

Philip Wiegratz

To find the speed of the fish when it hits the water, we can use the principle of conservation of energy. The potential energy the fish initially has will be converted into kinetic energy when it hits the water.

Let's calculate the potential energy of the fish initially:
Potential energy (PE) = mass * gravitational acceleration * height
PE = 2.00 kg * 9.8 m/s^2 * 5.40 m
PE ≈ 105.84 J

Now, we can equate this to the kinetic energy of the fish just before hitting the water:
Kinetic energy (KE) = 0.5 * mass * velocity^2

Since the fish is dropped, there is no initial velocity, so the equation can be simplified to:
PE = KE

105.84 J = 0.5 * 2.00 kg * velocity^2

Solving for velocity:
velocity^2 = (105.84 J) / (0.5 * 2.00 kg)
velocity^2 ≈ 52.92 m^2/s^2

Therefore, the speed of the fish when it hits the water is the square root of 52.92 m^2/s^2:
velocity ≈ √(52.92 m^2/s^2)
velocity ≈ 7.27 m/s

So, the speed of the fish when it hits the water is approximately 7.27 m/s.

To find the speed of the fish when it hits the water, we can use the principle of conservation of energy. The potential energy lost by the fish as it falls is converted into kinetic energy.

The potential energy of the fish is given by the equation:

Potential energy (PE) = mass (m) * gravity (g) * height (h)

Where:
- mass (m) of the fish is 2.00 kg
- gravity (g) is approximately 9.8 m/s^2 (acceleration due to gravity)
- height (h) is 5.40 m

So, the potential energy of the fish is:
PE = 2.00 kg * 9.8 m/s^2 * 5.40 m

Now, the potential energy is converted into kinetic energy (KE) as the fish falls:

PE = KE

Kinetic energy is given by the equation:

Kinetic energy (KE) = (1/2) * mass (m) * velocity^2

Where:
- mass (m) of the fish is 2.00 kg
- velocity of the fish is what we need to find

Now we can set up the equation:

PE = KE
2.00 kg * 9.8 m/s^2 * 5.40 m = (1/2) * 2.00 kg * velocity^2

Simplifying the equation:

98.00 kg*m^2/s^2 * 5.40 m = velocity^2

528.72 kg*m^2/s^2 = velocity^2

Taking the square root of both sides to solve for velocity:

velocity = sqrt(528.72 kg*m^2/s^2)

Calculating the value of velocity:

velocity ≈ 22.99 m/s

So, the speed of the fish when it hits the water is approximately 22.99 m/s.

The horizontal component is Vx = 18.0 m/s and the vertical component is

Vy = sqrt (2 g H)
H = 5.4 m
g = 9.8 m/s^2

The resultant speed is V = sqrt (Vx^2 + Vy^2)