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:

where’s the list ? the question is incomplete