Question

select the correct answer.
a ball is thrown straight down from the top of a building at a velocity of 16 ft/s. the building is 480 feet tall, and the acceleration due to gravity is 32 ft/s².
this problem can be represented using the following equation.
$\left(\frac{1}{2}\
ight) 32t^2 + 16t = 480$
how much time will the ball take to reach the ground?
a. 6 seconds
b. 5 seconds
c. 10 seconds
d. 15 seconds

Explanation:

Step1: Simplify the equation

$\frac{1}{2} \times 32t^2 + 16t = 480$ simplifies to $16t^2 + 16t = 480$. Divide all terms by 16: $t^2 + t = 30$. Rearrange to standard quadratic form: $t^2 + t - 30 = 0$.

Step2: Factor the quadratic

Find two numbers multiplying to -30 and adding to 1: 6 and -5. So, $(t + 6)(t - 5) = 0$.

Step3: Solve for t

Solutions are $t = -6$ or $t = 5$. Time can't be negative, so $t = 5$.

Answer:

B. 5 seconds