A bird is flying with a speed of 19.0 m/s over
water when it accidentally drops a 2.50 kg
fish.
The acceleration of gravity is 9.81 m/s^2
If the altitude of the bird is 9.00 m and air
resistance is disregarded, what is the speed of
the fish when it hits the water?
Answer in units of m/s
54
To find the speed of the fish when it hits the water, we can use the principle of conservation of energy.
The potential energy of the fish, when it is at an altitude of 9.00 m, can be calculated using the formula: PE = mgh, where m is the mass of the fish (2.50 kg), g is the acceleration due to gravity (9.81 m/s^2), and h is the altitude (9.00 m).
PE = (2.50 kg)(9.81 m/s^2)(9.00 m)
PE = 220.725 J
The potential energy is converted into kinetic energy as the fish falls. The kinetic energy is given by the formula: KE = (1/2)mv^2, where m is the mass of the fish and v is the speed of the fish when it hits the water.
Setting the potential energy equal to the kinetic energy:
PE = KE
220.725 J = (1/2)(2.50 kg)v^2
Now, solve for v:
v^2 = (2 * 220.725 J) / (2.50 kg)
v^2 = 441.45 J / 2.50 kg
v^2 = 176.58 m^2/s^2
Taking the square root of both sides:
v ≈ √(176.58 m^2/s^2)
v ≈ 13.29 m/s
Therefore, the speed of the fish when it hits the water is approximately 13.29 m/s.