Question

Need help on number 10 ONLY pleaseee!!

Answer 1

3/8 ( or 0.375) seconds.

Explanation:

When the ball hits the ground the height h = 0:

-16t^2 - 10t + 6 = 0

Solve for t:

-2(8t^2 + 5t - 3) = 0

-2(8t - 3 )(t + 1) = 0

t = 3/8 , - 1.

We ignore the -1.

So the time taken to reach the ground is 3/8 seconds.

Answer 2

0.375 sec

Explanation:

Given

h = - 16t² - 10t + 6

When the ball hits the ground h = 0, thus solve

- 16t² - 10t + 6 = 0 ← in standard form

Multiply through by - 1

16t² + 10t - 6 = 0

Consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 16 × - 6 = - 96 and sum = + 10

The factors are + 16 and - 6

Use these factors to split the t- term

16t² + 16t - 6t - 6 = 0 ( factor the first/second and third/fourth terms )

16t(t + 1) - 6(t + 1) = 0 ← factor out (t + 1) from each term

(t + 1)(16t - 6) = 0

Equate each factor to zero and solve for t

t + 1 = 0 ⇒ t = - 1

16t - 6 = 0 ⇒ 16t = 6 ⇒ t =
`(6)/(16)` = 0.375

However, t > 0 ⇒ t = 0.375

The ball takes 0.375 seconds to reach the ground