Chapter 1 - First-Order Differential Equations - 1.1 Differential Equations Everywhere - Problems - Page 12: 28

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Acceleration can be found by: $\frac{d^2y}{dt^2}=g$ Integrate: $\frac{dy}{dt}=gt+c_1\\\rightarrow y(t)=\frac{1}{2}gt^2+c_1t+c_2$ Since $y(0)=0$ and $\frac{dy}{dt}(0)=-2$ we have: $y(0)=0 \rightarrow c_2=0\\y(0)=-2 \rightarrow c_1=-2$ Substitute: $y(t)=\frac{1}{2}gt^2-2t\\ \rightarrow h=\frac{1}{2}g(10)^2-2(10)=470m$