Question

# A ball is thrown directly upward from a height of 3 ft with an initial velocity...

A ball is thrown directly upward from a height of 3 ft with an initial velocity of 20 ft/sec. the function s(t) = -16t^2+20t+3 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.

The given function

This is a qudratic function. The graph of the function represents a parabola comparing the function with we see that . and the parabola opens downwards since is negative.

Any parabola which opens downwards has its maximum height at the vertex. If we find the vertex of the parabola the co-ordinate which represent gives the time at the maximum heght and the co-ordinate that is represents the maximum height if the ball thrown upawards.

The co-ordinate of the parabola can be found by

Therefore the time in which the ball recahes the maximum height is Seconds.

Now to calculte the maximum height reached by the ball in Seconds we substitute the value of in the gievn function

Thererefore the maximum height reahed by the ball is

The figure shows the parabola

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