Answer:
Explanation:
The equation for the height h of the object after t seconds is given by:
h = -16t^2 + 145t + 2
To find when the height will be 230 feet, we can set h = 230 and solve for t:
230 = -16t^2 + 145t + 2
We can simplify this equation by moving all the terms to one side:
16t^2 - 145t + 228 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 16, b = -145, and c = 228. Plugging in these values, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)
t = (145 ± sqrt(21025 - 14592)) / 32
t = (145 ± sqrt(6433)) / 32
t ≈ 0.56 seconds or t ≈ 9.17 seconds
Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.
To find when the object will reach the ground, we can set h = 0 and solve for t:
0 = -16t^2 + 145t + 2
Again, we can simplify this equation by moving all the terms to one side:
16t^2 - 145t - 2 = 0
Using the quadratic formula again, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)
t = (145 ± sqrt(21249)) / 32
t ≈ 9.51 seconds or t ≈ 0.15 seconds
Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.
~~~Harsha~~~