Question

The height of an object dropped from a hot-air balloon can be determined by the formula h-161² +s, where h is the height of the object in feet, t is the elapsed time in seconds, and s is the height of the balloon. If the balloon is 400 feet from the ground, how long will it take for an object dropped from the balloon to hit the ground? ●2.5 seconds ●5 seconds ●7.5 seconds ● 10 seconds

Answer 1

To find the time that it will take for an object to hit the ground, consider that the ground has a height of 0.

Since the balloon is 400 feet from the ground and the heigh of the ground is h=0, substitute s=400 and h=0 into the equation and solve for t:

`\begin{gathered} h=-16t^2+s \\ \Rightarrow0=-16t^2+400 \\ \Rightarrow16t^2=400 \\ \Rightarrow t^2=(400)/(16) \\ \Rightarrow t^2=25 \\ \Rightarrow t=\sqrt[]{25} \\ \Rightarrow t=5 \end{gathered}`

Therefore, it would take 5 seconds for the object to hit the ground.