A package is dropped from a helicopter at a height of 310m. If it accelerates toward earth at 6.6m/s/s (due to air resistance) for the whole fall how much time will it take to hit the ground below?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![### Problem Statement
A package is dropped from a helicopter at a height of 310 meters. If it accelerates toward the Earth at 6.6 m/s² (due to air resistance) for the whole fall, how much time will it take to hit the ground below?
### Explanation and Solution
We need to determine the time it takes for the package to reach the ground.
Given:
- Initial height (h) = 310 meters
- Constant acceleration (a) = 6.6 m/s²
- Initial velocity (u) = 0 m/s (since the package is initially at rest)
We will use the second equation of motion:
\[ h = ut + \frac{1}{2} a t^2 \]
Substituting the given values:
\[ 310 = 0 \cdot t + \frac{1}{2} \cdot 6.6 \cdot t^2 \]
\[ 310 = 3.3 \cdot t^2 \]
\[ t^2 = \frac{310}{3.3} \]
\[ t^2 = 93.94 \]
\[ t = \sqrt{93.94} \]
\[ t \approx 9.7 \text{ seconds} \]
Therefore, the package will take approximately 9.7 seconds to hit the ground.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c4e41d9-a3ac-4d29-97cc-72954cf84754%2F51e7172b-20eb-42e2-adc7-d8a03c754c5a%2F6y2z6ja.png&w=3840&q=75)
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