Answer to Question #136147 in Physics for Andrea

Question

Salmon often jump waterfalls to reach their
breeding grounds.
Starting downstream, 2.95 m away from a
waterfall 0.54 m in height, at what minimum
speed must a salmon jumping at an angle of
29.7
◦
leave the water to continue upstream?
The acceleration due to gravity is 9.81 m/s
2
.
Answer in units of m/s.

Answer 1

Remembering that the horizontal component of velocity is constant, the range till the waterfall wall will be

$$2.95=v_xt=v\text{ cos}\theta \cdot t.$$

During the same time of flight, the salmon must reach the height of 0.54 m. This may be before or after the highest point of the trajectory:

$$0.54=v_yt-\frac{gt^2}{2}=v\text{ sin}\theta-\frac{gt^2}{2}.$$

So, we see that we have two equations with two unknowns: $v,t$. That is why the system of equations is solvable, solve it with any method you like (the most straightforward is substitution):

$$v=7.04\text{ m/s}\\ t=0.483\text{ s}$$