Question

Salmon often jump waterfalls to reach their breeding grounds. Starting downstream, 1.54 m away from a waterfall 0.547 m in height. at what minimum speed must a salmon jumping at an angle of 26.8º leave the water to continue upstream? The acceleration due to gravity is 9.81 m/s.

Answer 1

To continue upstream, a salmon must leave the water at a minimum speed of 3.62 m/s

Step-by-step explanation:

To calculate the minimum speed at which a salmon must jump to continue upstream, we can use the principle of conservation of energy. At the starting point, the salmon has gravitational potential energy, which is given by the formula PE = mgh, where m is the mass of the salmon, g is the acceleration due to gravity, and h is the height of the waterfall. This potential energy is converted into kinetic energy as the salmon jumps, and it can be expressed as KE = 0.5mv^2, where v is the velocity of the salmon. Setting the potential energy equal to the kinetic energy, we can solve for v:

mgh = 0.5mv^2

Canceling out the mass and rearranging the equation, we get:

v = sqrt(2gh)

Substituting in the known values of h = 0.547 m and g = 9.81 m/s^2, we can calculate the minimum speed:

v = sqrt(2 * 9.81 * 0.547) = 3.62 m/s

Therefore, the salmon must leave the water at a minimum speed of 3.62 m/s to continue upstream.