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Salmon often jump waterfalls to reach their
breeding grounds.
Starting downstream, 2.61 m away from a
waterfall 0.277 m in height, at what minimum
speed must a salmon jumping at an angle of
39.3° leave the water to continue upstream?
The acceleration due to gravity is 9.81 m/s.
Answer in units of m/s.


Sagot :

With the projectile launch we can find that the response for the initial velocity of the salmon is  3.68 m/s

Projectile launching is an application of kinematics for movement in two dimensions.  In this case they indicate the jump distance x = 2.61 m and the jump height y = 0.277 m and the angle of 39.3º and ask the initial velocity.

Let's use trigonometry for the initial velocity.

              cos 39.3 = [tex]\frac{v_x}{v}[/tex]

              sin 39.3 = [tex]\frac{v_y}{v}[/tex]

              vₓ = v cos 39.3

              = v sin 39.3

 

Suppose that when you reach the height of the waterfall you are in the highest part of the jump, therefore the vertical velocity is zero.

                [tex]v_y^2 = v_{oy}^2 -2 g y[/tex]

                 0 = - 2 g y

                 [tex]v_{oy}[/tex] = [tex]\sqrt{2gy}[/tex]

           

Let's calculate

                 [tex]v_{oy} = \sqrt{2 \ 9.8 \ 0.277}[/tex]

                  = 2.33 m / s

The relationship of the initial velocity and the angle.

                    = v sin 39.3

                   v = [tex]\frac{ v_{oy}}{son 39.3}[/tex]

                   v = 2.33 / sin 39.3

                   v = 3.68 m / s

               

In conclusion using projectile launch we can find the initial velocity of the salmon is 3.68 m / s.

Learn more here:  brainly.com/question/15063198