A) An object is dropped from a height of 20 feet off the ground. What is its velocity when it hits the ground? B) Instead of being dropped, the object is thrown down, such that when it is 20 feet off the ground, it already has an initial velocity of 20 ft/sec straight down. What is its velocity

Question

A) An object is dropped from a height of 20 feet off the ground. What is its velocity when it hits the ground?
B) Instead of being dropped, the object is thrown down, such that when it is 20 feet off the ground, it already has an initial velocity of 20 ft/sec straight down. What is its velocity when it hits the ground?
C) What did you assume in answering questions A and B? Give at least three examples of objects for which your assumptions are very good, and at least one example of an object for which your assumptions would fail badly.

Accepted Answer

A) Energy is conserved, so [latex]\Delta \mathrm{PE}+\Delta \mathrm{KE}=0[/latex] :

[latex]\begin{gathered}m g \Delta z+\frac{m \Delta u^{2}}{2}=0\\frac{\Delta u^{2}}{2}=-g \Delta z\0.5\left( u_{2}^{2}- u_{1}^{2} ight)=-g\left(z_{2}-z_{1} ight)\ u_{1}=0, z_{2}=0, so :\ u_{2}=\sqrt{2 g z_{1}}\ u_{2}=\sqrt{(2)\left(\frac{32.2 \,f t}{s^{2}} ight)(20 \,f t)}=35.9 \,f t / s\end{gathered}[/latex]

B) Energy is conserved, [latex]\Delta \mathrm{PE}+\Delta \mathrm{KE}=0[/latex] :

[latex]\begin{gathered} m g \Delta z+\frac{m \Delta u^{2}}{2}=0 \ g \Delta z+\frac{\Delta u^{2}}{2}=0 \ \frac{ u_{2}^{2}}{2}-\frac{ u_{1}^{2}}{2}=g\left(z_{1}-z_{2} ight) \ u_{2}^{2}=2 g\left(z_{1}-z_{2} ight)+ u_{1}^{2}, z_{2}=0 \ u_{2}=\sqrt{2 g\left(z_{1}-z_{2} ight)+ u_{1}^{2}} \ u=\sqrt{2\left(32.2 \,f t / s^{2} ight)(20 \,f t)+(20)^{2} \,f t^{2} / s^{2}}=41.1 \,f t / s\end{gathered}[/latex]

C) Air resistance was ignored. This is reasonable for most objects, but wouldn't work for something with a high surface area to mass ratio, such as a piece of paper or a feather.

Question 1.22: A) An object is dropped from a height of 20 feet off the gro...

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