(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In another universe, the force of gravity causes not a constant acceleration, but a constant "jerk" (third derivative of position with respect to time) with a value of j in the downward direction. An object is launched from the ground with an initial velocity of v_0 at an angle of theta and the initial acceleration is zero. Derive an expression for the horizontal distance the object will travel before it hits the ground. Answer in terms of theta, J, and v_0.

2. Relevant equations

3. The attempt at a solution

I know that

x = Ʃ[k=0,n] (x^(k)t^k)/k!

note that x^(k) is the kth derivative not kth power

so to come up with the equation were we consider the first three derivatives of x we got

x = x_0 + (dx/dt) t + 1/2 (d^2x/dt^2) t^2 + 1/6 (d^3x/dt^3)t^3

or

x = x_0 + v_0 t + 1/2 at^2 + 1/6 jt^3

in this case we want the horizontal component of the velocity so

x = x_0 + v_0 cos(θ) t + 1/2 at^2 + 1/6 jt^3

we are given that the initial acceleration is zero... so can I just ignore it completely from this problem sense it doesn't say to include air friction? This is what I assumed

x = x_0 + v_0 cos(θ) t + 1/6 jt^3

does this look correct?

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# Kinematics - Jerk Problem

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