Suppose an object is dropped from a height h0 above the ground. Then its height after t seconds is given by h = −16t 2 + h0, where h is measured in feet. Use this information to solve the problem.A ball is dropped from the top of a building 59 ft tall. (Round your answers to three decimal places.)(a) How long will it take to fall half the distance to ground level?t = sec(b) How long will it take to fall to ground level?t = sec
Accepted Solution
A:
Answer:Step-by-step explanation:Given[tex]h=-16t^2+h_0[/tex]ball is dropped from a height of [tex]59 ft[/tex]therefore [tex]h_0=59 ft[/tex][tex]h=-16t^2+59[/tex]Time taken to fall half the distance to the ground level i.e. [tex]h=\frac{59}{2}[/tex][tex]\frac{59}{2}=-16t^2+59[/tex]arranging we get[tex]16t^2=\frac{59}{2}[/tex][tex]t^2=\frac{59}{2\times 16}[/tex][tex]t=1.35 s[/tex](b)Time taken to fall i.e. h=0[tex]0=-16t^2+59[/tex][tex]16t^2=59[/tex][tex]t^2=\frac{59}{16}[/tex][tex]t=1.92 s[/tex]