微積分應用題，請問圈起來的題目怎麼解-－jpjzhf9的部落格

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微積分應用題，請問圈起來的題目怎麼解?

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(a) 英制, 重力加速度 = 32 ft / s^2 h = 256 - (1/2)*32*t^2 = 256 - 16*t^2 落地時, h = 0 , 所以: 0 = 256 - 16*t^2 t^2 = 256/16 = 16 t = 4 (b) tan θ = h / 500 = ( 256 - 16*t^2 ) / 500 等式兩邊對 t 微分, 等式恆成立: sec^2 θ * dθ/dt = - (16/500)*2t = - 8t / 125 dθ/dt = - cos^2 θ * 8t / 125 When t = 1 h = 256 - 16 = 240 cos^2 θ = 500^2 / ( 500^2 + 240^2 ) = 250000/307600 = 625/769 dθ/dt = - (625/769) * 8/125 = - 40/769 When t = 2 h = 256 - 16*4 = 192 cos^2 θ = 500^2 / ( 500^2 + 192^2 ) = 250000/286864 = 15625/17929 dθ/dt = - (15625/17929) * 8*2/125 = - 2000/17929 Ans: (a) h = 256 - 16*t^2 4 秒時落地 (b) 當 t = 1 , dθ/dt = - 40/769 當 t = 2 , dθ/dt = - 2000/17929

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