How Do You Calculate the Initial Drop Height in a Free Fall Problem?

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In summary, a stone is dropped from rest off the science building and accelerates towards the ground at 9.8 m/s/s. A physics student observes the stone falling past a 2.2 m tall window in 0.30 seconds and sketches a velocity vs. time plot. The average velocity of the stone as it falls past the window is 2.2/0.3 m/s and its velocity at the top of the window is 8.99999 m/s. The height from which the stone started its fall cannot be determined with the given information.
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runningirl
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Homework Statement



A stone is dropped off the science building and accelerates, from rest, toward the ground at 9.8 m/s/s. A curious physics student looks out the third floor window as the stone falls past. She happens to have a stopwatch and she finds that it takes 0.30 sec for the stone to fall past the 2.2 m tall window. She then sketches the velocity vs. time plot shown below, but realizing she is late for lunch, she doesn't use the plot to analyze the motion of the stone.

a) What was the average velocity of the stone as it fell past the window?

b) What was the velocity of the stone at the top of the window?

c) From what height above the top of the window did the stone start its fall?

Homework Equations



delta(x)=initial velocity*time + .5(at^2)

The Attempt at a Solution



a) I got 2.2/.3 m/s

b) I used the equation above and got 8.99999 m/s

c) I was clueless with part C
 
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  • #2
If a stone starts from rest, over what distance must it fall so that reaches a final speed of 2.2/3 m/s? That's the distance you re looking for.
 

Related to How Do You Calculate the Initial Drop Height in a Free Fall Problem?

1. What is velocity and why is it important?

Velocity is a physical quantity that describes the speed and direction of an object's motion. It is important because it allows us to understand how quickly an object is moving and in what direction, which can help us predict its future position and behavior.

2. How is velocity different from speed?

Velocity includes both the speed of an object and its direction of motion, while speed only refers to the rate at which an object is moving. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction, while speed is a scalar quantity with only magnitude.

3. What are the units of velocity?

The units of velocity depend on the system of measurement being used. In the International System of Units (SI), velocity is measured in meters per second (m/s). In the United States Customary Units, velocity is measured in feet per second (ft/s) or miles per hour (mph).

4. How is velocity calculated?

Velocity is calculated by dividing the displacement of an object by the time it took to travel that distance. This is represented by the equation v = d/t, where v is velocity, d is displacement, and t is time.

5. How does velocity relate to acceleration?

Velocity and acceleration are closely related. Acceleration is the rate of change of velocity over time. This means that if an object's velocity is changing, it is accelerating. When an object's velocity remains constant, it is not accelerating. In other words, acceleration is the derivative of velocity with respect to time.

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