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Answer :
Final answer:
To find out when the pebble will hit the ground, we solve the quadratic equation [tex]0 = -16t^2 + 24t + 900[/tex] to get the time in seconds which will be a positive value.
Explanation:
To determine how long after the pebble is thrown it will hit the ground, we need to find the value of t when the height h is 0, because the pebble hits the ground when its height above the ground is 0 feet. The equation we can use for this scenario is [tex]h = -16t^2 + 24t + 900[/tex]. Setting h to 0, we need to solve the quadratic equation [tex]0 = -16t^2 + 24t + 900[/tex] for t.
Using the quadratic formula,
[tex]t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a},[/tex] where a is -16, b is 24, and c is 900, we can find the time when the pebble hits the ground. Plugging in these values and solving for t will give us two solutions, one positive and one negative. We can ignore the negative solution as time cannot be negative, and the positive solution will be the time in seconds it takes for the pebble to hit the ground.
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Answer:
The pebble will hit the ground 8.29 second after it is thrown.
Step-by-step explanation:
Given that,
The height of the pebble after t seconds is given by the equation
h= -16t²+24 t+900.
When the pebble hit the ground, the height of the pebble will be zero.
So putting h=0 in the given equation.
0 = -16t²+24 t+900
⇒-4(4t²-6t-225)=0
⇒4t²-6t-225=0
Applying quadratic formula [tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex], here a=4, b= -6 and c= -225.
[tex]\therefore t=\frac{-(-6)\pm\sqrt{(-6)^2-4.4.(-225)}}{2.4}[/tex]
⇒ t = 8.29, -6.79
Since time can not negative.
∴t=8.29 seconds.
The pebble will hit the ground 8.29 second after it is thrown.
