中五 maths 幾條問題 ..@oo－gpjqem1的部落格

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中五 maths 幾條問題 ..@oo

發問:

(a) The radius of a sphere is r at time t. Find the radius when the rate ofincrease of the surface area and the rate of increase of the radius arenumerically equal.[Hint: Surface area of a sphere, S=4兀r^2](b) An object is projected verically under gravity. It height h is given by h=25t-5t^2where... 顯示更多 (a) The radius of a sphere is r at time t. Find the radius when the rate of increase of the surface area and the rate of increase of the radius are numerically equal. [Hint: Surface area of a sphere, S=4兀r^2] (b) An object is projected verically under gravity. It height h is given by h=25t-5t^2 where t=time in second, and h is in metre. (i) Find the height it reaches at time t=2 seconds. (ii) Find its velocity at time t=2 seconds. (iii) Find its acceleration at time t=2 seconds. (iv) Find the maximum height reached. [Hint: at maximum height, its velocity is zero.]

最佳解答:

(a) S=4πr^2,dS/dt=(8πr)(dr/dt) Let dS/dt=dr/dt (8πr)(dr/dt)=dr/dt 8πr=1 r=1/8π (b)(i) h(2)=25t-5(2)^2=25-20=5 m (ii) h'(t)=25-10t=>h'(2)=5 m/s (iii) h''(t)=-10=>h''(2)=-10 ms^-2 (iv) Let h'(t)=0=>t=2.5. h(2.5)=25*2.5-5(2.5)^2=31.25 m

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