A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.901.90 s. You may ignore air resistance, so the brick is in free fall. How tall, in meters, is the building?

Identify the known values: The initial velocity (v₀) is 0 m/s, the time (t) is 1.90 s, and the acceleration due to gravity (g) is approximately 9.81 m/s². Use the kinematic equation for displacement in free fall: d=$$v_{0}$t+12gt^2. $$Since the initial velocity is zero, the equation simplifies to d=$$12gt^2. $$Substitute the known values into the simplified equation: d=$$12(9.81)(1.90)^2. $$Calculate the expression inside the parentheses: First, square the time, $$1.90^2$$, then multiply by the acceleration due to gravity, 9.81. Multiply the result by 12 to find the displacement, which is the height of the building.

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problem 42a

Chapter 2, Problem 42a

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in $1.90$ s. You may ignore air resistance, so the brick is in free fall. How tall, in meters, is the building?

Verified step by step guidance

Identify the known values: The initial velocity (v₀) is 0 m/s, the time (t) is 1.90 s, and the acceleration due to gravity (g) is approximately 9.81 m/s².

Use the kinematic equation for displacement in free fall:

d = v

₀t+12gt^2. Since the initial velocity is zero, the equation simplifies to

d = \frac{1}{2} g t^2

Substitute the known values into the simplified equation:

d = \frac{1}{2} (9.81) (1.90)^2

Calculate the expression inside the parentheses: First, square the time,

1.90^2

, then multiply by the acceleration due to gravity,

9.81

Multiply the result by

\frac{1}{2}

to find the displacement, which is the height of the building.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Free Fall

Free fall refers to the motion of an object under the influence of gravitational force only, with no other forces acting on it, such as air resistance. In this scenario, the brick is in free fall, meaning it accelerates downward at a constant rate due to gravity, which is approximately 9.81 m/s² on Earth.

Acceleration Due to Gravity

Acceleration due to gravity is the rate at which an object speeds up as it falls freely towards the Earth. It is denoted by 'g' and has a standard value of 9.81 m/s². This constant acceleration is crucial for calculating the distance an object falls over a given time when air resistance is negligible.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. For free fall, the equation h = 0.5 * g * t² can be used to find the height from which an object is dropped, where 'h' is the height, 'g' is the acceleration due to gravity, and 't' is the time taken to reach the ground.

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Textbook Question

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