Trajectory

Question

Suppose a Chinook salmon needs to jump a waterfall that is 1.50m high. If the fish starts from a distance of 1.00 m from the base of the ledge over which the waterfall flows, 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. Can the fish make the jump? (Remember that a Chinook salmon can jump out of the water with a speed of 6.26m/s^2.)

Answer 1

Hi Mara F., I'll sketch the path to solution.

1) Assume the fish takes off as implied: 1 m lateral, 1.5 m vertical, at specified velocity. Use trig functions to decompose that velocity into x- and y- vectors (v(x,0), v(y,0)).

2) Figure time until fish achieves the lateral distance. Note that v(x) doesn't change over time (unless the fish doesn't make it!)

3) The y-component follows a standard y = y(0)[=0] + v(0,y)*t - 0.5 g t^2 . Plug your time from step (2) in, and figure where the fish is vertically at that time.

4) If it's >1.5 m, the fish made it. If not, you need to install a "fish ladder".

-- Cheers, -- Mr. d.

P.S. If the salmon konks itself out, or if it's post-spawning and dead or dieing, do not eat it raw or especially allow your dog to do so. See "salmon poisoning"!