Use the given information to answer the question. The distance s that an object falls varies directly with the square of the time, t, of the fall. If an object falls 16 feet in one second, how long will it take for it to fall 80 feet? Round your answer to two decimal places. It will take ...... seconds for the object to fall 80 feet.

Answer

2.24 seconds for the object to fall 80 feet.

Q: What is the direct variation formula? A: The direct variation formula is y=kx, where k is the constant of variation.
Q: How can we apply the formula to this problem? A: We have s=k t^2 and s=16 when t=1. Plug in these values to solve for k: k=s/t^2=16/1=16. Therefore, s=16t^2.
Q: How long will it take for the object to fall 80 feet? A: We have s=80, so 80=16t^2. Solving for t, we get t=sqrt(80/16)=2.24.