Salmon often jump waterfalls to reach their
breeding grounds.
starting downstream, 1.95 m away from a
waterfall 0.311 m in height, at what minimum
speed must a salmon jumping at an angle of
37.7° leave the water to continue upstream?
the acceleration due to gravity is 9.81 m/s2.
answer in units of m/s.

5.0 m/s

Explanation:

The horizontal motion of the salmon is uniform, so the horizontal component of the salmon's velocity is constant and it is

where u is the initial speed and . The horizontal distance travelled by the salmon is

where d = 1.95 m and t is the time needed to reach the final point.

Re-arranging for t,

(1)

Along the vertical direction, the equation of motion is

where:

y = 0.311 m is the final height reached by the salmon

h = 0 is the initial height

is the vertical component of the initial velocity of the salmon

is the acceleration of gravity

t is the time

Substituting t as found in eq.(1), we get the equation

and we can solve this formula for u, the initial speed of the salmon: