Question

Salmon often jump waterfalls to reach their breeding grounds. Starting downstream, 1.99 m away from a waterfall 0.468 m in height, at what minimum speed must a salmon jumping at an angle of 30° leave the water to continue upstream? The acceleration due to gravity is 9.81 m/s.

a) 5.18 m/s
b) 6.36 m/s
c) 4.23 m/s
d) 7.89 m/s

Answer 1

The minimum speed at which the salmon must leave the water to continue upstream is 4.23 m/s.

Step-by-step explanation:

To determine the minimum speed at which the salmon must leave the water, we can use the conservation of energy. The potential energy at the top of the waterfall is equal to the kinetic energy when the salmon jumps. Using the equation:

PE = KE
mgh = (1/2)mv^2

Where m is the mass of the salmon, g is the acceleration due to gravity, h is the height of the waterfall, and v is the velocity of the salmon. We can solve for v to find the minimum speed:

v = √2gh

Substituting the given values, we get:

v = √(2 * 9.81 m/s^2 * 0.468 m) = 4.23 m/s

Therefore, the minimum speed at which the salmon must leave the water to continue upstream is 4.23 m/s. Option c) 4.23 m/s is the correct answer.