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Lady_Fox [76]
3 years ago
14

A ball is kicked in the air. The height of the ball can be calculated using the equation h(t) =-16t^2+64t+190, where h is in hei

ght in feet and t is time in seconds. Find the time it takes for the ball to strike the ground
Mathematics
1 answer:
gregori [183]3 years ago
5 0

Answer:

Therefore the ball strikes the ground  5.98 s after kick.          

Step-by-step explanation:

Given that , a ball is kicked in the air. The height of the ball can be calculated using the equation h(t)=-16t^2+64t+190    where h is height in feet and t is time in second.

When the ball touches the ground then the height will be zero.

i.e h(t)=0

Therefore

-16t^2+64t+190=0

\Rightarrow -2(8t^2-32t-95)=0

Since -2≠0 then (8t^2-32t-95)=0

(8t^2-32t-95)=0    

[The solution of a quadratic equation ax²+bx+c=0 is

  x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}  here a=8, b=-32 and c=-95]                    

\Rightarrow t =\frac{-(-32)\pm\sqrt{(-32)^2-[4\times8\times(-95)]} }{2\times8}        

\Rightarrow t =\frac{32\pm\sqrt{4064} }{16}    

Therefore   t=  5.98 or -1.98

since time can not be negative So , t=5.98 s

Therefore the ball strikes the ground  5.98 s after kick.          

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