for the following question, use the function h = - 16t² + v₀t + h₀, where h is the height of the object…

for the following question, use the function h = - 16t² + v₀t + h₀, where h is the height of the object after time t, v₀ is the initial velocity, and h₀ is the initial height. an object is thrown upward from a height of 1344 ft with an initial velocity of 80 ft/ s. how long will it take for the object to reach the ground?

for the following question, use the function h = - 16t² + v₀t + h₀, where h is the height of the object after time t, v₀ is the initial velocity, and h₀ is the initial height. an object is thrown upward from a height of 1344 ft with an initial velocity of 80 ft/ s. how long will it take for the object to reach the ground?

Answer

Explanation:

Step1: Substitute values into formula

Given $h_0 = 1344$, $v_0=80$, and at ground $h = 0$. So the equation becomes $0=-16t^{2}+80t + 1344$.

Step2: Simplify the equation

Divide the entire equation by -16: $t^{2}-5t - 84=0$.

Step3: Factor the quadratic equation

We factor $t^{2}-5t - 84$ as $(t - 12)(t+7)=0$.

Step4: Solve for t

Set each factor equal to zero: $t - 12=0$ gives $t = 12$; $t+7=0$ gives $t=-7$. Since time cannot be negative in this context, we discard $t=-7$.

Answer:

$12$