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?
See
http://www.jiskha.com/display.cgi?id=1285261758
i still don't understand parts b and c.
(b)
let u = velocity at the top of the window.
In t=0.3 second, the object has travelled -2.2 m with an acceleration of g=-9.8 m/s².
Use the kinematic equation
S(distance)=ut+(1/2)gt²
Solve for u to get
u=S/t-(1/2)gt
=-2.2/0.3-(-9.8)/2*0.3
= the same expression Mr.Pursley gave.
(c)
Equate potential and kinetic energies to get
mgh=(1/2)mu²
where u is obtained from (b) above.
Solve for h.
To answer these questions, we need to use the equations of motion and the given information. Let's break down each question and find the answers step by step.
A) What was the average velocity of the stone as it fell past the window?
The average velocity can be calculated using the formula:
Average Velocity = Total Displacement / Total Time
We know that the stone fell a distance of 2.2 meters and it took 0.30 seconds to fall past the window. Using these values, we can plug them into the formula:
Average Velocity = 2.2 meters / 0.30 seconds
Calculating this, we get:
Average Velocity = 7.33 m/s
So, the average velocity of the stone as it fell past the window is 7.33 m/s.
B) What was the velocity of the stone at the top of the window?
To find the velocity of the stone at the top of the window, we can use the equation of motion:
Final Velocity = Initial Velocity + (Acceleration * Time)
The stone starts from rest, so the initial velocity is 0 m/s. The acceleration due to gravity is -9.8 m/s^2 (negative because it acts downwards) and the time taken is 0.30 seconds. Plugging these values into the equation, we get:
Final Velocity = 0 m/s + (-9.8 m/s^2 * 0.30 s)
Calculating this, we get:
Final Velocity = -2.94 m/s
So, the velocity of the stone at the top of the window is -2.94 m/s. The negative sign indicates that the stone is moving downward.
C) From what height above the top of the window did the stone start its fall?
To find the height above the top of the window where the stone started its fall, we can use the kinematic equation:
Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance
The final velocity is 0 m/s (as the stone comes to rest when it hits the ground). The initial velocity is also 0 m/s (as the stone starts from rest). The acceleration is -9.8 m/s^2 and we need to find the distance.
Rearranging the equation, we get:
Distance = (Final Velocity^2 - Initial Velocity^2) / (2 * Acceleration)
Plugging in the values, we have:
Distance = (0 m/s - 0 m/s) / (2 * -9.8 m/s^2)
Calculating this, we get:
Distance = 0 meters
Therefore, the stone started its fall from the top of the window.
In summary:
A) The average velocity of the stone as it fell past the window is 7.33 m/s.
B) The velocity of the stone at the top of the window is -2.94 m/s.
C) The stone started its fall from the top of the window.