A rescue plane is flying horizontally at a height of 132 m above the ground. The pilot spots a survivor and releases an emergency kit with a parachute. The kit descends at a constant vertical acceleration of and the initial plane horizontal speed is . Assuming air resistance and wind are negligible, how long will the emergency kit be falling through the air?
Please read and clarify your problem.
What is the vertical acceleration?
To find the time it takes for the emergency kit to fall through the air, we can use the kinematic equation:
h = ut + (1/2)gt^2
Where:
h = height of the kit above the ground (132 m)
u = initial vertical velocity of the kit (0 m/s, as it starts from rest)
g = acceleration due to gravity (-9.8 m/s^2, assuming downward direction)
t = time taken for the kit to fall
Since the kit is falling downward, the acceleration is negative.
Plugging in the known values, we can rearrange the equation to solve for t:
132 = 0*t + (1/2)*(-9.8)*t^2
Simplifying the equation:
132 = -4.9*t^2
Dividing both sides by -4.9:
t^2 = -132 / -4.9
t^2 = 26.9388
Taking the square root of both sides:
t ≈ √26.9388
t ≈ 5.19 s
Therefore, the emergency kit will be falling through the air for approximately 5.19 seconds.