Answer:
D
Step-by-step explanation:
When the ball hits the ground then h = 0 , that is
- 5t² + 13t + 6 = 0 ( multiply through by - 1 )
5t² - 13t - 6 = 0
Consider the factors of the product of the coefficient of the h² term and the constant term which sum to give the coefficient of the h- term.
product = 5 × - 6 = - 30 and sum = - 13
The factors are - 15 and + 2
Use these factors to split the h- term
5t² - 15t + 2t - 6 = 0 ( factor the first/second and third/fourth terms )
5t(t - 3) + 2(t - 3) = 0 ← factor out (t - 3) from each term
(t - 3)(5t + 2) = 0
Equate each factor to zero and solve for t
t - 3 = 0 ⇒ t = 3
5t + 2 = 0 ⇒ 5t = - 2 ⇒ t = - [tex]\frac{2}{5}[/tex]
Now t > 0 , so t= 3
The ball hits the ground after 3 seconds
