A stone is dropped from a height of $9$ meters above the ground. If the height functions can be modeled by the equation $h (t) = a - t^{2}$ , where $t$ is the time in seconds, $h$ is height in meters, and a is the initial height, how many seconds does it take for the stone to hit the ground?

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Solution

Initial height of stone (at t=0) $= 9 m = h (0)$

$\Rightarrow h (0) = a - 0^{2}$

$\Rightarrow a = 9$

Let 't' be the time taken to reach the ground

When it reaches the ground height =0

$\Rightarrow 0 = 9 - t^{2}$

$∴ t = 3$ seconds

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A stone is dropped from a height of 9 meters above the ground. If the height functions can be modeled by the equation h(t)=a−t2, where t is the time in seconds, h is height in meters, and a is the initial height, how many seconds does it take for the stone to hit the ground?

Initial height of stone (at t=0)=9m=h(0)⇒h(0)=a−02⇒a=9Let 't' be the time taken to reach the ground When it reaches the ground height =0⇒0=9−t2∴t=3 seconds

A stone is dropped from a height of $9$ meters above the ground. If the height functions can be modeled by the equation $h (t) = a - t^{2}$ , where $t$ is the time in seconds, $h$ is height in meters, and a is the initial height, how many seconds does it take for the stone to hit the ground?

Initial height of stone (at t=0) $= 9 m = h (0)$

$\Rightarrow h (0) = a - 0^{2}$

$\Rightarrow a = 9$

Let 't' be the time taken to reach the ground

When it reaches the ground height =0

$\Rightarrow 0 = 9 - t^{2}$

$∴ t = 3$ seconds