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A rocket on a computer screen has a path modeled by the equation \(h=-t^2+3t+10\) where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.

A 5 seconds.

The platform is reached when h = 0. It is necessary to solve the equation \(0=-t^2+3t+10\). Hence (t - 5)( t + 2) = 0. Solving the equation gives t = 5 or -2. As t is a time it is not possible for t to be -2. The rocket takes 5 seconds to reach the platform.

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