Solve the problem. Round to the nearest tenth, if necessary. A rock falls from a tower that is 432 feet high. As it is falling, its height is given by the formula h = 432 - 16t2. How many seconds will it take for the rock to hit the ground (h=0)?
0 = 432 - 16 t^2
t^2 = 432/16
t = (1/4) sqrt (16*27)
t = sqrt 27 which is about 5.2 seconds
To find the number of seconds it will take for the rock to hit the ground, we need to solve the equation h = 0.
Substituting h = 0 into the given formula, we get:
0 = 432 - 16t^2
Rearranging the equation and isolating the variable, we have:
16t^2 = 432
Divide both sides of the equation by 16:
t^2 = 27
To solve for t, take the square root of both sides:
t = ±√27
However, since time cannot be negative in this context, we only consider the positive square root:
t ≈ √27
Calculating the square root, we get:
t ≈ 5.2
Therefore, it will take approximately 5.2 seconds for the rock to hit the ground.
To find the number of seconds it will take for the rock to hit the ground, we need to set the height equation h = 0 and solve for t.
The height equation is given as h = 432 - 16t^2, where h is the height and t is the time in seconds.
Setting h = 0, we have:
0 = 432 - 16t^2
Now, let's solve for t:
Subtracting 432 from both sides of the equation:
-432 = -16t^2
Dividing both sides of the equation by -16:
t^2 = 27
Taking the square root of both sides of the equation:
t = √27
Now, let's simplify the square root:
t = √(9 * 3)
t = 3√3 ≈ 5.20
Therefore, it will take approximately 5.2 seconds for the rock to hit the ground.