Grantham PHY220 Week 2 Assignment Problem 4

A not so brilliant physics student wants to jump from a 3rd-floor apartment window to the swimming pool below. The problem is the base of the apartment is 8.00 meters from the pool’s edge. If the window is 20.0 meters high, how fast does the student have to be running horizontally to make it to the pool’s edge?

Solution:

Since the student will be running horizontally, there is no initial vertical velocity, v_{0_y}=0. We are also given \Delta x=8\:m, and \Delta y=-20\:m.

Consider the vertical component of the motion.

\Delta y=v_{0_y}t-\frac{1}{2}gt^2

-20=0-\frac{1}{2}\left(9.80\right)t^2

-20=-4.9t^2

t^2=\frac{20}{4.9}

t=\sqrt{\frac{20}{4.9}}

t=2.02\:s

Consider the horizontal component of the motion

\Delta x=v_{0_x}t

v_{0_x}=\frac{\Delta x}{t}

v_{0_x}=\frac{8}{2.02}

v_{0_x}=3.96\:m/s

Therefore, the student should be running 3.96 m/s horizontally to make it to the pool’s edge.

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