Police at a crime scene find a ceramic mug shattered on the sidewalk. They want to determine the window from which the mug fell, and they decide to make a model of the fall. Which quantity would be an important boundary condition for this model?
A. The initial height of the mug above the sidewalk.
B. The hardness of the sidewalk where the mug landed.
C. The final speed of the mug.
D. The time of day when the incident occurred.
Thanks guys, the answer was actually B though.
I think the answer is A or C
thx
To determine the window from which the mug fell, the police are creating a model of the fall. In this scenario, a boundary condition is a value or parameter that must be specified to fully define the problem.
Out of the given options, the most important boundary condition for this model would be:
A. The initial height of the mug above the sidewalk.
By knowing the initial height of the mug, the police can calculate the time it takes for the mug to fall and estimate the horizontal distance it would travel. This information is crucial in determining the location of the window from which the mug fell.
Let's say the police know the height from which the mug fell, they can use the laws of physics, specifically kinematics equations, to find the time it took for the mug to reach the sidewalk along with other information like the horizontal distance it traveled.
For instance, the equation for calculating the time of fall for an object in free-fall is:
t = sqrt(2h/g)
Where:
t = time of fall
h = initial height of the mug above the sidewalk
g = acceleration due to gravity (approximately 9.8 m/s² on Earth)
By plugging in the known value of the initial height, the police can calculate the time it took for the mug to fall. This information will help narrow down the possible window locations.
In summary, the initial height of the mug above the sidewalk is the most important boundary condition for the model the police are creating to determine the window from which the mug fell.