A freely falling object hit the ground in 18𝑎! seconds. It fell ℎ feet. Use the formula ℎ = 16𝑡! to find ℎ in terms of 𝑎.
To find the height ℎ in terms of 𝑎, we can substitute the value of time 𝑡 in the given equation ℎ = 16𝑡² with the value of time 𝑡 = 18𝑎, since the object hits the ground in 18𝑎 seconds.
Let's substitute the value of 𝑡 in terms of 𝑎 into the equation:
ℎ = 16(18𝑎)²
Now, let's simplify the equation to find the final expression for 𝑎 in terms of ℎ:
ℎ = 16(324𝑎²)
ℎ = 5184𝑎²
Therefore, the height ℎ of the freely falling object, in terms of 𝑎, can be written as ℎ = 5184𝑎².