Answer :
Answer:
5.03 m
Explanation:
Let the distance of burglar from the top of window be [tex]x[/tex] m.
Given:
Displacement of the bag while passing the window, [tex]h=-1.6[/tex] m
Time to cross the window, [tex]t=0.15[/tex] s
Acceleration due to gravity,[tex]g=-9.8[/tex] m/s²(∵ it acts down)
Negative sign indicates downward motion and hence negative.
We find the velocity of the bag at the top of the window using Newton's equation of motion for displacement.
[tex]h=ut+\frac{1}{2}at^2[/tex]
Where, [tex]u[/tex] is the velocity at the top of window.
Now, plug in all the known values and solve for [tex]u[/tex].
[tex]-1.6=u(0.15)+\frac{1}{2}(-9.8)(0.15)^2\\-1.6=0.15u-0.11\\0.15u=-1.6+0.11\\0.15u=-1.49\\u=\frac{-1.49}{0.15}=-9.93\textrm{ }m/s^2[/tex]
Now, from the point of drop to the top of the window, displacement is [tex]x[/tex]. Initial velocity is zero as it is dropped. Acceleration is due to gravity. Final velocity is velocity at the top of window which is equal to -9.93 m/s².
Therefore, using Newton's equation of motion [tex]v_{f}^2-v_{i}^2=2ax[/tex], we find [tex]x[/tex].
Here, [tex]v_{f}=-9.93,v_{i}=0,a=g=-9.8[/tex]
Therefore,
[tex]x=\frac{v_{f}^2-v_{i}^2}{2a}\\x=\frac{(-9.93)^2-0}{2(-9.8)}\\x=\frac{98.6}{-19.6}=-5.03\textrm{ m}[/tex]
The negative sign indicates that the bag is falling down.
So, the bag is dropped at a height of 5.03 m from above the top of the window.