Asked by Lily
The equation y = -16t^2 + 26t + 105 describes the height (in feet) of a ball tossed up in the air at 26 feet per second from a height of 105 above the ground. In how many seconds will the ball hit the ground? express your answer as a decimal rounded to the nearest tenth.
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Answered by
GPT 3.5
To find out when the ball will hit the ground, we need to find the time when the height (y) is equal to 0.
Setting y = 0 in the equation, we get:
0 = -16t^2 + 26t + 105
This is a quadratic equation that can be solved using the quadratic formula:
t = (-26 ± √(26^2 - 4(-16)(105))) / (2(-16))
t = (-26 ± √(676 + 6720)) / (-32)
t = (-26 ± √7396) / (-32)
t = (-26 ± 86) / (-32)
Now we have two possible solutions:
t = (-26 + 86) / -32 = 60 / -32 = -1.875
t = (-26 - 86) / -32 = -112 / -32 = 3.5
The positive solution, 3.5 seconds, is the time it takes for the ball to hit the ground.
Setting y = 0 in the equation, we get:
0 = -16t^2 + 26t + 105
This is a quadratic equation that can be solved using the quadratic formula:
t = (-26 ± √(26^2 - 4(-16)(105))) / (2(-16))
t = (-26 ± √(676 + 6720)) / (-32)
t = (-26 ± √7396) / (-32)
t = (-26 ± 86) / (-32)
Now we have two possible solutions:
t = (-26 + 86) / -32 = 60 / -32 = -1.875
t = (-26 - 86) / -32 = -112 / -32 = 3.5
The positive solution, 3.5 seconds, is the time it takes for the ball to hit the ground.
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