The function s(t) = 16t^2 models the distance, s(t), in feet, that an object falls in t seconds. Find the number of seconds a sky diver is in free fall after jumping from a plane if she falls 192 feet before opening a parachute. Express your answer in simplified radical form.
16t^2=192
16t^2/16=192/16
t^2=12
square roote of t^2 = the square root of 12
To find the number of seconds a sky diver is in free fall after falling 192 feet, we can set up the equation:
16t^2 = 192
Divide both sides of the equation by 16:
t^2 = 12
To find t, we can take the square root of both sides:
t = √12
Simplifying the square root of 12:
t = √(4 * 3)
Breaking the square root of 4 and 3 apart:
t = √4 * √3
Since the square root of 4 is 2, we can simplify further:
t = 2√3
Therefore, the skydiver is in free fall for 2√3 seconds after jumping from a plane.
To find the number of seconds a sky diver is in free fall after falling 192 feet, we need to solve the equation 16t^2 = 192.
Step 1: Rearrange the equation
Divide both sides of the equation by 16 to isolate t^2:
t^2 = 192/16
t^2 = 12
Step 2: Take the square root
To solve for t, we need to take the square root of both sides of the equation:
√(t^2) = √12
t = ±√12
Since time cannot be negative in this context, we take the positive square root and get:
t = √12
Step 3: Simplify the radical form
√12 can be simplified as follows:
√12 = √(4 × 3) = √4 × √3 = 2√3
Therefore, the number of seconds the sky diver is in free fall is 2√3 seconds.