A stone is thrown from the top of a building with an initial velocity of 24.6 m/s downward. The top of the building is 59.2 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground?
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.
![**Projectile Motion Problem: Calculating Time of Descent**
*A stone is thrown from the top of a building with an initial velocity of 24.6 m/s downward. The top of the building is 69.2 m above the ground. How much time elapses between the instant of release and the instant of impact with the ground?*
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**Explanation:**
In this problem, you need to determine the time it takes for the stone to reach the ground after it is thrown from the top of the building. The given parameters are:
- Initial velocity (\(v_0\)): 24.6 m/s downward
- Height of the building (\(h\)): 69.2 m
Use the following kinematic equation to solve for time (\(t\)):
\[ h = v_0 t + \frac{1}{2} g t^2 \]
where
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).
*Step-by-step solution can be provided as needed for the students to understand the computations involved in solving the quadratic equation to find the time of descent.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa023f3c3-3186-4c61-aa74-30f5825e9d0f%2F00cabe3b-eebb-43fc-a8d5-cbf1d1e51d46%2Fian0qvo.jpeg&w=3840&q=75)
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