A boy stands on the edge of a cliff of height 60m. He throws a stone vertically upwards so that its distance, h, above the cliff top is given by `h...

Friday, February 13, 2015

The given function is:

$\displaystyle{h}{\left({t}\right)}={20}{t}-{5}{{t}}^{{2}}$

where h(t) represents the height of the stone above the cliff.

Since the cliff is 60m above the sea, when the stone hits the beach, the value of h(t) is -60. Plugging this value, the function becomes:

$\displaystyle-{60}={20}{t}-{5}{{t}}^{{2}}$

Take note that to solve quadratic equation, one side should be zero.

$\displaystyle{5}{{t}}^{{2}}-{20}{t}-{60}={0}$

The three terms have a GCF of 5. Factoring out 5, the equation becomes:

$\displaystyle{5}{\left({{t}}^{{2}}-{4}{t}-{12}\right)}={0}$

Dividing both sides by 5, it simplifies to:

$\displaystyle{{t}}^{{2}}-{4}{t}-{12}={0}$

Then, factor the expression at the left side of the equation.

$\displaystyle{\left({t}-{6}\right)}{\left({t}+{2}\right)}={0}$

Set each factor equal to zero. And isolate the t.

$\displaystyle{t}-{6}={0}$

$\displaystyle{t}={6}$

$\displaystyle{t}+{2}={0}$

$\displaystyle{t}=-{2}$

Since t represents the time, consider only the positive value. (Let's assume that the time t is in seconds.) So the value of t when h(t)=-60 is:

$\displaystyle{t}={6}$

Therefore, the stone hits the beach 6 seconds after it was thrown.

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