select the correct answer. a ball is thrown s...
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. (1/2)32t² + 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
Answer
# Explanation:
## Step1: Simplify the given equation
The given equation is $\frac{1}{2}\times32t^{2}+16t = 480$. First, simplify $\frac{1}{2}\times32t^{2}$ to get $16t^{2}+16t = 480$. Then divide the entire equation by 16, resulting in $t^{2}+t - 30=0$.
## Step2: Solve the quadratic - equation
For a quadratic equation $ax^{2}+bx + c = 0$ (here $a = 1$, $b = 1$, $c=-30$), we can use the quadratic formula $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ or factor the equation. Factoring $t^{2}+t - 30=0$ gives $(t + 6)(t - 5)=0$.
## Step3: Find the values of t
Setting each factor equal to zero: $t+6 = 0$ gives $t=-6$ and $t - 5=0$ gives $t = 5$. Since time cannot be negative in this context, we discard $t=-6$.
# Answer:
B. 5 seconds