Answer:
v = 7.65 m/s
t = 0.5882 s
Explanation:
We are told that the salmon started downstream, 3.18 m away from a waterfall.
Thus, range = 3.18 m
Since the horizontal velocity component is constant, then;
Range = vcosθ × t
Thus,
vcosθ × t = 3.18 - - - (eq 1)
We are told the salmon reached a height of 0.294 m
Thus, using distance equation;
s = v_y•t + ½gt²
g will be negative since motion is against gravity.
s = v_y•t - ½gt²
Thus;
0.294 = v_y•t - ½gt²
v_y = vsinθ
Thus;
0.294 = vtsinθ - ½gt² - - - (eq 2)
From eq(1), making v the subject, we have;
v = 3.18/tcosθ
Plugging into eq 2,we have;
0.294 = (3.18/tcosθ)tsinθ - ½gt²
0.295 = 3.18tanθ - ½gt²
We are given g = 9.81 m/s² and θ = 45°
0.295 = (3.18 × tan 45) - ½(9.81) × t²
0.295 = 3.18 - 4.905t²
3.18 - 0.295 = 4.905t²
4.905t² = 2.885
t = √2.885/4.905
t = 0.5882 s
Thus;
v = 3.18/(0.5882 × cos45)
v = 7.65 m/s
