Question

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 height in feet and t is time in seconds. Find the time it takes for the ball to strike the ground

Answer 1

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.