Question

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, 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 this jump? (Remember that a Chinook salmon can jump out of the water with a speed of 6.26 m/s.)

Could someone please help me with this question? Thanks alot

Answer 1

How much energy does it take to go 1.5m?

mgh=m*9.8*1.5= 14.7m joules
How much KE does the fish have initially?
1/2 m v^2= 1/2 m (6.26^2)=19.6m
Well, there is plenty of energy to go that high. So, will the fish go that high and still land 1m kupstream?

At the top , vvertical is zero. So how long will the fish take to fall that same distance?
vvertical= vverticalinitial-gt
0=6.26sinTheta-gt
This is the same time it takes to get to the top, so
t= 6.26sinTheta/g

How far does the fish travel hoizontally in that time?
1=6.26cosTheta*t
= 6.26costheta*6.26sinTheta/g

solvefor theta. Remember 2cosAsinA=sin2A
If you get an angle, the fish can do it.