Sam and Sarah have taken their math textbooks to the top of a 12 story building and look at the pool which is 160 straight below them. Sam..?

2014-07-27 10:28 pm
just lets go of his book, while Sarah throws her book down with an initial velocity of 48 feet per second. How many seconds does it take each book to hit the water?

回答 (3)

2014-07-28 12:34 am
For Sam, The object hits the ground when its position is s(t) = 0. Set the position equation equal to zero and solve for t.

The position equation is s(t) = 16t^2 + v(o)t + h(o)
In Sam's case, v(o) = 0 and h(o) is 160ft.
2014-07-28 12:02 am
Sam
16t^2 = 160 --->t = 3.2s
Sarah
16t^2+48t=160 --->t=2s
2014-07-28 12:00 am
The pool is 160 below them?
Well...
160 miles or inches? I'm gonna assume that's 160 feet as that's about the corresponding height for a 12-story building.
I'll take acceleration of the Earth as 32.2 ft/s^2

Then use the displacement equation.
s = Vi*t + at^2 / 2
Using a as g, let's solve for Sam's book.
The initial V is 0, so the eq. is:
s = gt^2 / 2
160 ft = (32.2 ft/s^2)*t^2 / 2 = 3.15 s

Now Sarah (this will evolve into a quadratic equation):
160 ft = (48 ft/s)*t + (32.2 ft/s^2)*t^2 / 2
16.1t^2 + 48t - 160 = 0
t = ( -48 +-root(48^2 - 4*16.1*(-160)) ) / (2*16.1) = 2 s or -4.98 s.

After 2 s you hear splash #1 from Sarah, while it takes 3.15 s for Sam's book to get wet.

Best wishes!


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