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2026-02-13

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cole physics problem 2: escape from burning building

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another physics problem from cole.

your friend, a world-class jumper, is trapped on the roof of a burning building. his only escape route is to jump to the roof of the next building. fortunately for him, he is in telephone contact with you,a physics 161 student, for advice on how to proceed. he has two options. he can jump to the next building by using the long-jump technique where he jumps at 45° to the horizontal. or, he can take his chances by staying where he is in the hopes that the fire department will rescue him. you learn from the building engineers that the next building is 10 m away horizontally and the roof is 3 m below the roof of the burning building. you also know that his best long-jump distance is 7.9 m. what do you advise him to do?
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From Cole. PHYS161 Discussion. 1&2-D Kinematics. Units 1 and 2

jumping at 45°. the vertical and horizontal components of $v_{0}$ are thus $\frac{v_{0}}{\sqrt{2}}$ .

\begin{matrix} s_{x} t & = (real v_{0}) t \\ s_{y} t & = (imag v_{0}) t + \frac{1}{2} g t^{2} . \end{matrix}

solve $s_{x} t = 7.9$ for $t$

$s_{x} (\frac{7.9 \sqrt{2}}{| v_{0} |}) = 7.9$

use that value in

$s_{y} (\frac{7.9 \sqrt{2}}{| v_{o} |}) = 0$

NOW we know $| v_{0} | = \sqrt{- 7.9 g}$ or $v_{0} = \sqrt{- 7.9 g} e^{\frac{i τ}{8}}$ .

cole physics problem 3: skydivers

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cole physics

attachment:clipboard-20260213T214122.png

the MC skydiving club has asked you to plan a stunt for an air show. in this stunt, two skydivers will step out of opposite sides of a stationary hot air balloon 5 000 ft above the ground. the second skydiver will leave the balloon 20 seconds after the first skydiver, but you want them both to land on the ground at the same time. the show is planned for a day with no wind so you may assume all motion is vertical. to get a rough idea of the situation assume that a skydiver will fall with a constant acceleration of 32 ft/s² before the parachute opens. as soon as the parachute opens, the skydiver falls with a constant speed of 10 ft/s. if the first skydiver, sue, waits 3 seconds after dropping out of the balloon before opening her parachute, how long must the second skydiver, joe, wait after leaving the balloon before opening the parachute

find when sue's parachute line intersects with free fall line to get

$a = 0.1875 \sqrt{561} + 20.3125$

then uhhh set

\begin{matrix} 5000 + \frac{1}{2} (- 32) 3^{2} + (a - 3) (- 10) \\ = & 5000 + \frac{1}{2} (- 32) t_{B}^{2} + (a - t_{B} - 20) (- 10) \end{matrix}

and sove for $t_{B}$ to get $t_{B} = 0.1875 \sqrt{561} + 0.3125 \approx 4.75351$ .