i found out how to do part a and b but i do not know how to solve for c when the

Question

i found out how to do part a and b but i do not know how to solve for c when the acceleration is not constant.

A package is dropped from a flying airplane. Assume that the gravity is g 9.81 m/s2 constant. For the first 10 seconds, the parachute is not deployed, and you can ignore any air resistance. (a) Find the vertical velocity and the vertical distance it has dropped at the end of the 10 seconds. You may just use the constant acceleration formulas learned in physics Ans (a) 98 mls 410.5 m At the end of the 10 seconds, the parachute pops and the y acceleration of the package becomes a (9.81 -0.01v) m/s Reset the clock at this moment. You may also reset the y coordinate there to zero. (b) Determine the time it takes for the vertical velocity to reach v 500 m/s Ans (b) 6o.T35 s (c) Determine the vertical distance ittravels in part (b). Ans: (c) l 9,39 l m

Explanation / Answer

Here ,

c) after the fist 10 s

velocity = 98.1 m/s

NOw, let the distance is x

as a = v dv/dx

v dv/dx = 9.81 - 0.01 v

v/(9.81 - 0.01v)dv = dx

integrating

integrate(v/(9.81 - 0.01v)dv) from 98.1 to 500 = integrate(dx) from 0 to x

solving

x = 19390.5 m

hence , the correct answer is 19390.5 m

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