Salmon often jump waterfalls to reach their breeding grounds. starting downstream, 2.33 m away from a waterfall 0.488 m in height, at what minimum speed must a salmon jumping at an angle of 38 ◦ leave the water to continue upstream? the acceleration due to gravity is 9.81 m/s 2

5.68 m/s

Explanation:

The motion of the salmon is the same as a projectile: it is launched with an initial speed at an angle of above the horizontal.

The motion of the salmon consists of two indipendent motion:

- Along the horizontal direction, it is a uniform motion with constant velocity

So that the distance travelled is

(1)

- Along the vertical direction, it is a uniformly accelerated motion with constant acceleration downward, so the vertical displacement is

(2)

where g is the acceleration of gravity.

We know the following:

- The horizontal distance travelled by the salmon to reach the waterfall is

d = 2.33 m

- The vertical distance travelled is the height of the waterfall,

y = 0.488 m

From (1) we get:

And substituting into (2), we can solve the equation to find t, the time at which the salmon reaches the waterfall:

And then, we can use eq.(1) again to find the initial speed, u:

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