If an object is thrown vertically upward, the height (h) at any time (t) is given by: h = 16t^2+vt
A package is thrown downward w/initial velocity of -5 ft/sec. from a helicopter at 300 ft. What is the height of the package in 2 sec and how long does it take to hit the ground.
When an object is thrown vertically upward, the height at any time t is given by the expression h = 16*t^2 + v*t.
If a package is thrown downward from a helicopter at 300 ft with an initial velocity 5 ft/s, the height of the package after 2 seconds is:
300 - (16*2^2 + 5*2) = 300 - 74 = 226 ft.
The time taken by the package to hit the ground is the solution of 300 - (16*t^2 + 5*t) = 0
=> 16t^2 + 5t - 300 = 0
The positive solution of this equation is `(5*sqrt(769)-5)/32` s
The height of the package in 2 seconds is 226 ft and it takes `(5*sqrt(769)-5)/32` s to strike the ground.