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King Fahad University of Petroleum & Minerals Problem Design

King Fahad University of Petroleum & Minerals Problem Design Non-linear Air Resistance Group # 4 Bin Mahfoud , Saud Faisal Malawi, Ahmad Al Osaimi , Saad Radhwan , Ayman AL Hadi,Mohammad. Non-linear Air Resistance Problem # 16, Page # 110.

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King Fahad University of Petroleum & Minerals Problem Design

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  1. King Fahad University of Petroleum & Minerals Problem Design Non-linear Air Resistance Group # 4 Bin Mahfoud, Saud Faisal Malawi, Ahmad Al Osaimi, SaadRadhwan, Ayman AL Hadi,Mohammad

  2. Non-linear Air Resistance Problem # 16, Page # 110 • In this problem a cannonball is shot vertically upward • How High? We are asked to find the maximum height. Given that V = 300ft/s at t = 0 Fresα V2 Fres= KV2

  3. Non-linear Air ResistanceProblem # 16, Page # 110 Ftotal = KV2+ W Where W is the weight of the ball, V is the instantaneous velocity and K 0.0003 We have F = ma where a= dv/dt So we have dv/dt =-(+KV2 + W)/m

  4. Solve, we get • t = -49/12*3^(1/2)*atan(1/400*V*3^(1/2))+ C Using the boundary condition C= 6.4696 • t at V = 0 (Max.hight) t= 6.4696 sec.

  5. V vs t (Time)

  6. We can use V = ds/dt , where S is the traveled distance. • We get S= -353625/433*log(1+tan(400/2829*t)^2)+C Using the boundary Condition S=0 At t = 0 C = 0 Use t = 6.4696 sec then we get S = 807.4091meter.

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