Question

A ball is thrown from the top row of seats in a stadium. The function

Answer 1

Answer:

It will be 5 seconds before the ball hits the ground  

Step-by-step explanation:

∵ A ball is thrown from the top row of seats in a stadium

∵ The function

∵ h(t) = −16t² + 64t + 80 , gives the height, in feet, of the ball t seconds

   after it is thrown

∵ The ball hits the ground

→ That means h(t) = 0

∵ h(t) = 0

∴ 0 = -16t² + 64t + 80

→ Reverse the two sides

∴ -16t² + 64t + 80 = 0

→ Divide both sides by -16 to simplify it

∵  $\frac{-16t^{2}}{-16}+\frac{64t}{-16}+\frac{80}{-16}=\frac{0}{-16}$

∴ t² - 4t - 5 = 0

→ Factorize it into two factors

∵ t² = t × t

∵ -5 = -5 ×  1

∵ -5t + 1t = -4t ⇒ the middle term

→ The factors are (t - 5) and (t + 1)

∴ (t - 5)(t + 1) = 0

→ Equate each factor by 0 to find t

∵ t - 5 = 0

→ Add 5 to both sides

∴ t = 5

∵ t + 1 = 0

→ Subtract 1 from both sides

∴ t = -1 ⇒ rejected because no negative value for the time

∵ t = 5

∴ It will be 5 seconds before the ball hits the ground