A Stone is thrown downward from a height of 900 feet with a velocity of 30 ft/sec. Find its distance above the ground after *t* seconds. What is its velocity after 5 seconds? When will it strike the ground? What it's velocity be when it hits the ground?

Guest Nov 15, 2018

#1**+1 **

We have this

H = -16t^2 - 30t + 900

Where H is the height after t seconds

The derivative of this is the velocity

H' = -32t - 30

After 5 seconds, the velocity is

-32(5) - 30 =

-190 ft/ s

To find the time to hit the ground....set H = 0

-16t^2 - 30t + 900 = 0

-8t^2 - 15t + 450 = 0

8t^2 + 15t - 450 = 0

The positive solution to this is ≈ 6.62 sec

The velocity at this time is -32(6.62) - 30 ≈ -241.8 ft/sec

CPhill
Nov 15, 2018

#3**0 **

Approx 330 fps is ARROW velocity from a compound bow.....that rock is moving! In reality, air friction will keep it from coming down that fast!

Terminal velocity for a body thrown out of an airplane (think skydiver) is ~ 120 mph , which is

120 m/hr x 5280 ft/m x 1hr/3600s = 120*5280/3600 = 176 ft/sec (been there, done that) just an FYI..... ~ EP

ElectricPavlov
Nov 16, 2018