A football is punted into the air. Its height is modeled by the equation
h=-4.9t^2+21.6t+1.3, in metres and seconds. Determine the amount of time the football is in the air before it hits the ground. Round to the nearest
tenth of a second.
wrong yet again,
The two roots are -0.058 and 4.467
Surely you should realize that it's not reasonable for the ball to hit the ground in 1/5 of a second!
Apologies for the mistake in my previous response.
To find the amount of time the football is in the air before it hits the ground, we need to find the value of t when the height of the football is equal to 0.
Setting the equation h = 0:
0 = -4.9t^2 + 21.6t + 1.3
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -4.9, b = 21.6, and c = 1.3.
Plugging in these values into the quadratic formula, we get:
t = (-21.6 ± √(21.6^2 - 4 * -4.9 * 1.3)) / (2 * -4.9)
Simplifying the expression inside the square root:
t = (-21.6 ± √(466.56 + 25.36)) / (2 * -4.9)
t = (-21.6 ± √491.92) / (2 * -4.9)
Taking the square root:
t = (-21.6 ± 22.178) / (2 * -4.9)
Now, we can evaluate both solutions:
t₁ = (-21.6 + 22.178) / (2 * -4.9) ≈ 4.467
t₂ = (-21.6 - 22.178) / (2 * -4.9) ≈ -0.058
Since time cannot be negative in this context, we can ignore the negative solution.
Therefore, the amount of time the football is in the air before it hits the ground is approximately 4.5 seconds (rounded to the nearest tenth of a second).
To determine the amount of time the football is in the air before it hits the ground, we need to find the value of t when h = 0.
We have the equation: h = -4.9t^2 + 21.6t + 1.3
Setting h to 0, the equation becomes:
0 = -4.9t^2 + 21.6t + 1.3
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -4.9, b = 21.6, and c = 1.3. Plugging in these values, we have:
t = (-21.6 ± √(21.6^2 - 4*(-4.9)*1.3)) / (2*(-4.9))
Calculating this equation will give us two values for t. However, we only need the positive value since time cannot be negative.
t ≈ 4.5 seconds
Therefore, the football is in the air for approximately 4.5 seconds before it hits the ground.
To find the amount of time the football is in the air before it hits the ground, we need to find the value of t when the height of the football is equal to 0.
We can set the equation h = 0 and solve for t:
0 = -4.9t^2 + 21.6t + 1.3
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not easy, so we'll use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -4.9, b = 21.6, and c = 1.3.
Plugging these values into the quadratic formula, we get:
t = (-21.6 ± √(21.6^2 - 4 * -4.9 * 1.3)) / (2 * -4.9)
Simplifying the expression inside the square root:
t = (-21.6 ± √(466.56 + 25.36)) / (2 * -4.9)
t = (-21.6 ± √491.92) / (2 * -4.9)
Taking the square root:
t = (-21.6 ± 22.18) / (2 * -4.9)
Now, we can evaluate both solutions:
t₁ = (-21.6 + 22.18) / (2 * -4.9) ≈ 0.221
t₂ = (-21.6 - 22.18) / (2 * -4.9) ≈ -1.951
Since time cannot be negative in this context, we can ignore the negative solution.
Therefore, the amount of time the football is in the air before it hits the ground is approximately 0.221 seconds (rounded to the nearest tenth of a second).