A projectile is shot vertically up in the air from ground level. Its distance h, in feet, after t seconds is given by h = 96t – 16t2. Find the values of t when h is 96 feet?

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May you please the quadratic formula. Or if you use some other way please explain it to me.

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Answer 1 · 2018-03-23T12:24:23

#t=3+sqrt(3)#

#t=3-sqrt(3)#

So we have the height as a function of #t#:

#f(t)=96t-16t^2#

#:.#

#h=96t-16t^2#

When the projectile is 96 feet above the ground, we have:

#96=96t-16t^2#

#-16t^2+96t-96=0#

We need to solve this for #t#

We can make this easier by reducing the coefficients:

Divide through by #-16#

#t^2-6t+6=0#

#(-b+-sqrt(b^2-4ac))/(2a)#

We have:

#a=1#

#b=-6#

#c=6#

Plugging in these values:

#(-(-6)+-sqrt((-6)^2-4(1)(6)))/(2(1))#

#(6+-sqrt(36-(24)))/(2)#

#(6+-sqrt(12))/2=(6+-2sqrt(3))/2=3+-sqrt(3)#

#t=3+sqrt(3)#

#t=3-sqrt(3)#