Question 980034
{{{ h(t) = -4.9t^2 + 29.4t }}}
(a)
{{{ t = 2 }}}
{{{ h(2) = -4.9*2^2 + 29.4*2 }}}
{{{ h(2) = -19.6 + 58.8 }}}
{{{ h(2) = 39.2 }}} m
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{{{ t = 3 }}}
{{{ h(3) = -4.9*3^2 + 29.4*3 }}}
{{{ h(3) = -44.1 + 88.2 }}}
{{{ h(3) = 44.1 }}} m
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(b)
The horizontal coordinate of the max height
is at {{{ t[max] = -b/(2a) }}} where
{{{ a = -4.9 }}}
{{{ b = 29.4 }}}
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{{{ t[max] = -29.4 / (-9.8 ) }}}
{{{ t[max] = 3 }}} sec
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The max height is at {{{ h(3) = 44.1 }}} m
as already shown
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(c)
The ball hits the ground when {{{ h(t) = 0 }}}
{{{ -4.9t^2 + 29.4t  = 0 }}}
{{{ t*( -4.9t + 29.4 ) = 0 }}}
{{{ 4.9t = 29.4 }}}
{{{ t = 6 }}}
The ball hits the ground in 6 sec
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(d)
The range is {{{ 0 }}} to {{{ 44.1 }}}
The domain is {{{ 0 }}} to {{{ 6 }}}
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Here's the plot:
{{{ graph( 400, 400, -1, 7, -5, 50, -4.9x^2 + 29.4x ) }}}