How would this equation 016t21600 change if the helicopter c

How would this equation 0=-16t²+1600 change if the helicopter copilot THREW the package down at an initial velocity of 80 ft/sec? Please show all work in steps.

Solution

The equation 0= - 16t²+1600 gives the time t (in seconds) in which an object thrown with zero initial velocity from a height of 1600 ft. falls freely to the ground.

We know that the height/ velocity relationship for an object falling towards the earth from an initial height of h₀ feet with an initial velocity of v₀ ft/s is h(t) = - (g /2) t² + v₀ t + h₀ = =-16t²+v₀t+h₀ ( as g = 32ft/s² ) , where h(t) is the height of the object after t seconds.

Thus, if the helicopter copilot threw the package down at an initial velocity of 80 ft/sec, then the time taken by the package to hit the ground will be given by the equation 0 = -16t² +80t + 1600.