When an object is dropped from a height of $h$ feet, the time it will take to hit the ground can be approximated by the formula $\quad t=\sqrt{\frac{3 h}{5}}$
where $t$ is the time in seconds for the object to fall $h$ feet. If you want an object to fall for 6 seconds, from what height should the object be dropped? \{your final answer only number, no units required \}
Answer
Final Answer: \(\boxed{60}\)
Step 1 ：Given that the time for the object to fall is 6 seconds, we can substitute this into the rearranged formula for height.
Step 2 ：The rearranged formula for height is \( h = \frac{5t^2}{3} \).
Step 3 ：Substituting \( t = 6 \) into the formula, we get \( h = \frac{5 \cdot 6^2}{3} \).
Step 4 ：Solving the equation gives \( h = 60.0 \).
Step 5 ：So, the object should be dropped from a height of 60 feet for it to fall for 6 seconds.
Step 6 ：Final Answer: \(\boxed{60}\)
