The height, h, in metres, above the ground of a football t seconds after it is thrown can be modelled by the function h(t)= -4.9t^2 + 19.6t + 2. Determine how long the football will be in the air, to the nearest tenth of a second.
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The football is in the air as long as h is a positive number. Thus, when the height is zero, the ball has hit the ground. The key is to find what positive value of t (what time) yields a zero value for h.
To solve this problem, set the function modeling the height of the ball equal to zero.
Now, either using a graphing calculator or the quadratic formula (-b plus or minus the square root of (b^2 - 4ac), all divided by 2a), you can solve for t. You should get t = 4.0995626. If you plug this into the equation, you should get h = 0.
Since you want the answer to the nearest tenth of a second, the final answer is 4.1 seconds.
To solve this problem, set the function modeling the height of the ball equal to zero.
Now, either using a graphing calculator or the quadratic formula (-b plus or minus the square root of (b^2 - 4ac), all divided by 2a), you can solve for t. You should get t = 4.0995626. If you plug this into the equation, you should get h = 0.
Since you want the answer to the nearest tenth of a second, the final answer is 4.1 seconds.
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You have to substitute 0 for height to find out how long until it has a height of zero. Then, you just solve for the time.