Question 1158564: Scott and Tommy are glad to be done with algebra. The climb to the roof of a 300 foot building. Emmett drops his algebra book while Brennan throws his towards the ground at 10 feet per second. What is the time difference between the two books hitting the ground?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The height as function of elapsed time for an object's vertical motion near the earth's surface using the fps measurement system is:
\ =\ -16t^2\ +\ v_ot\ +\ h_o)
Where ) represents the height at time  ,  is one-half of the gravitational acceleration constant near the earth,  is the initial velocity of the object, and  is the initial height of the object.
For both experiments, the initial height,  , and the gravitational acceleration constant is, as the name implies, a constant.
For one of these hooligans showing egregious disrespect for their algebra textbooks, the initial velocity is  . This value is negative because "...towards the ground...". For the other, the initial velocity is zero.
When the books hit the ground, the height is zero. Hence, you need to solve the following two quadratic equations to determine the values of  , the elapsed time for the book thrown and  , the elapsed time for the book dropped so that you can make the final calculation of  , which answers the question posed.
^2\ -\ 10t_T\ +\ 300\ = 0)
^2\ +\ 300\ = 0)
The rest is just arithmetic.
Extra Credit
Which book hits the ground first if one just drops his and the other throws his UPWARDS at 10 feet per second?
John
My calculator said it, I believe it, that settles it
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