+0  
 
0
226
3
avatar

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?

 Nov 15, 2018
 #1
avatar+111357 
+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

 

 

cool cool cool

 Nov 15, 2018
 #2
avatar
0

Thanks

Guest Nov 16, 2018
 #3
avatar+23494 
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

10 Online Users

avatar