/sci/ - Science & Math

>>11396610
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>>11396758
I like this one c:
>>11396714
You can't neglect air resistance in this situation. The drag force on the person would be [math] F_d=C_dA\rho v^2/2 [/math]. If the person normally can normally jump a height [math] h [/math] then they are airborne for [math]t=\sqrt{2h/g} [/math] seconds; assume they have a mass [math] m [/math], then the total distance they would be pushed backward during their jump with respect to the roof of the car would be [math] F_dt^2/2m [/math] or [eqn] \text{distance pushed backward by air resistance}=\frac{C_d A\rho v^2h}{2mg} [/eqn]
I will leave it to you to plug in values! Hint: A is about 0.7 square meters.
>>11396764
>What about using partial derivatives?
Not sure what you mean. You use partial derivatives when you propagate error. Say you have a calculation that depends on N measurements [math] f(x_1,x_2,..,x_N) [/math] and each measurement has an uncertainty [math]u_i[/math]. Then to a first order approximation, the total uncertainty of [math] f [/math] is [eqn] u_{total}=\sqrt{\sum_{i=1}^N\Bigg(\frac{\partial f}{\partial x_i}u_i\Bigg)^2} [/eqn]