An osprey flying horizontally 100 feet above a lake spots a fish below. It tilts its flight path downward by 45°. If the osprey is diving at 45 mph, at what rate is its altitude changing (rounded to the nearest foot per second)?

the rate at which its altitude is changing is -47 ft/s

Step-by-step explanation:

Given that;

ds/dt = 45 mph =  45 × 5280/3600 = 66 ft/sec

no we have to determine dx/dt

so

cos∅ = dx/dt / ds/dt

cos45° = dx/dt / 66  

dx/dt = 0.7071 × 66

dx/dt = 46.6686 ≈ 47 ft/s ( as altitude is decreasing, its negative - )

so the rate at which its altitude is changing is -47 ft/s

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step-by-step explanation: