Answer: 6.2 m/s
Explanation:
1) This is a projectile motion (parabolic)
2) Velocity:
i) initial velocity = V₀
ii) Horizontal component:
V₀x = V₀ cos α
The horizontal velocity is constant, so Vx = V₀x
ii) Vertical component:
V₀y = V₀ sin α
The vertical component is linear with acceleration = g ≈ 9.8 m/s²
Vy = V₀y - gt = V₀ sin α - gt
3) Displacement equations
i) Horizontal displacment:
x = V₀ cosα t
ii) Vertical displacement:
y = V₀ sin α t - g t² / 2
y ≈ V₀ sin α t - 4.9 t²
4) Solution
i) x = V₀ cosα t = V₀ cos(32°) t = 2.00 m ← salmon starts 2.00m from a waterfall
⇒ V₀ = 2 / [cos(32°) t ]
ii) y = V₀ sin α t - 4.9 t² = V₀ sin(32°) t - 4.9 t²
iii) Replace V₀ with 2 / [cos(32°) t ]
y = sin(32°) × 2 / [cos(32°) t ] × t - 4.9t² = 2 tan(32°) - 4.9t²
iv) Use jump's height (y = 0.55m) and solve
⇒ 0.55 = 2 tan(32°) - 4.9t²
t² = [2 tan(32°) - 0.55 ] / 4.9 = 0.143 s²
⇒ t = √ (0.143s²) = 0.38 s
v) Use V₀ = 2 / [cos(32°) t ] to find V₀
V₀ = 2 / [cos(32°) (0.38) ] = 6.2 m/s
