Final answer:
The life preserver takes approximately 3.06 seconds to hit the water.
Step-by-step explanation:
To calculate how long the life preserver takes to hit the water, we can use the equations of motion. Since the helicopter is hovering, the initial velocity of the life preserver is 0 m/s. The final velocity is the velocity at which the life preserver hits the water. We can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration (which is equal to the acceleration due to gravity, approximately 9.8 m/s²), and t is the time taken. Rearranging the equation, we have:
t = (v - u) / a
Since v = 0 m/s and u = 0 m/s, the equation simplifies to:
t = - u / a
Given that the life preserver was dropped from a height of 30 meters below the helicopter, we can calculate the time taken:
t = - 30 m / -9.8 m/s² = 3.06 seconds