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# Physics with Differential Calculus

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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
+111357
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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

Nov 15, 2018
#2
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Thanks

Guest Nov 16, 2018
#3
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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