Salmon often jump waterfalls to reach their
breeding grounds.
starting downstream, 2.02 m away from a
waterfall 0.574 m in height, at what minimum
speed must a salmon jumping at an angle of
32 ◦
leave the water to continue upstream?
the acceleration due to gravity is 9.81 m/s
2
.
answer in units of m/s.

6.35 m/s

Explanation:

The motion of the salmon is equivalent to that of a projectile, which consists of two independent motions:

- A horizontal motion with constant speed

- A vertical motion with constant acceleration (, acceleration of gravity)

The horizontal velocity of the salmon is given by:

where

u = ? is the initial speed

is the angle of projection

Then the horizontal distance covered by the salmon after a time t is given by

Or equivalently, the time taken to cover a distance d is

(1)

Along the vertical direction, the equation of motion is

(2)

where

is the initial vertical velocity

If we substitute (1) into (2), we get:

We now that in order to reach the breeding grounds, the salmon must travel a distance of

d = 2.02 m

reaching a height of

h = 0.574 m

Substituting these data into the equation and solving for u, we find the initial speed that the salmon must have:

the arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.