an object is thrown upward from the top of an 80 ft tower. the height h of the object after t seconds is…
an object is thrown upward from the top of an 80 ft tower. the height h of the object after t seconds is represented by the quadratic equation h = -16t² + 64t + 80. after how many seconds will the object hit ground?\n\no 29 seconds\n\no 6.4 seconds\n\no 5.0 seconds\n\no 8.0 seconds
Answer
Explanation:
Step1: Set height h to 0
When the object hits the ground, $h = 0$. So we have the equation $-16t^{2}+64t + 80=0$.
Step2: Divide by -16
Divide the entire equation by - 16 to simplify: $t^{2}-4t - 5=0$.
Step3: Factor the quadratic
Factor the quadratic equation: $(t - 5)(t+1)=0$.
Step4: Solve for t
Set each factor equal to zero: $t - 5=0$ gives $t = 5$ and $t+1=0$ gives $t=-1$. Since time cannot be negative in this context, we discard $t=-1$.
Answer:
C. 5.0 seconds