An adult dolphin weighs around 1560 N. How fast must he be moving as he leaves the water vertically in order to jump to a hei

ght of 3.50 m? Ignore air resistance.

the weight is not a factor

1/2 m v^2 = m g h

v = √(7 g)

4.65

To find the speed at which the adult dolphin must be moving vertically as it leaves the water, we can use the principles of conservation of energy. We can equate the initial kinetic energy of the dolphin to the final potential energy at its maximum height.

The kinetic energy (KE) of an object is given by the formula:

KE = 0.5 * mass * velocity^2

In this case, the mass of the dolphin is not provided directly, but we are given its weight, which is 1560 N. Weight is the force exerted by gravity on an object, and it is related to mass by the formula:

weight = mass * gravity

where gravity is approximately 9.8 m/s^2 on Earth.

Rearranging the equation, we can solve for the mass of the dolphin:

mass = weight / gravity

Substituting the given values, we have:

mass = 1560 N / 9.8 m/s^2 = 160 kg

Now, at the maximum height of 3.50 m, the potential energy (PE) of the dolphin is given by the formula:

PE = mass * gravity * height

Substituting the known values:

PE = 160 kg * 9.8 m/s^2 * 3.50 m = 5488 J

Since the initial kinetic energy will be equal to the final potential energy, we can equate the formulas:

0.5 * mass * velocity^2 = PE

Substituting the known values:

0.5 * 160 kg * velocity^2 = 5488 J

Simplifying the equation:

80 kg * velocity^2 = 5488 J

Dividing both sides by 80 kg:

velocity^2 = 68.6 m^2/s^2

Taking the square root of both sides:

velocity ≈ √(68.6) m/s ≈ 8.28 m/s

Therefore, the dolphin must be moving vertically at a speed of approximately 8.28 m/s as it leaves the water in order to jump to a height of 3.50 m.