   Chapter 3, Problem 27P

Chapter
Section
Textbook Problem

Suppose a chinook salmon needs to jump a waterfall that is 1.50 m high. If the fish starts from a distance 1.00 m from the base of the ledge over which the waterfall flows, (a) find the x- and y-components of the initial velocity the salmon would need to just reach the ledge at the top of its trajectory, (b) Can the fish make this jump? (Note that a Chinook salmon can jump out of the water with an initial speed of 6.26 m/s.)

(a)

To determine
The x and y components of the initial velocity the salmon would need to just reach the ledge at the top of its trajectory.

Explanation

The path the salmon must follow is a parabolic path and the motion is a projectile motion. So, the vertical component is zero at the maximum height.

The vertical component of the initial velocity can be found from the kinematic equation,

vy2=v0y2+2ayΔy

Here,

vy is the vertical component of the velocity

v0y is the vertical component of the initial velocity

ay is the vertical acceleration

Δy is the vertical displacement

The vertical component of the initial velocity when the vertical displacement is 1.50m is,

v0y=vy22ayΔy

Substitute 0m/s for vy , 9.80m/s2 for g and 1.50m for Δy .

v0y=02(9.80m/s2)(1.50m)=5.42m/s

The time taken for the upward flight is,

Δt=vyv0yay

Substitute 0m/s for vy , 9

(b)

To determine
If the salmon could make the jump.

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