Question

h(t)= 20t-4.9t^2

Answer 1

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Answer 2

[AI-generated answer — Explain Bot]

The given equation is h(t) = 20t - 4.9t^2.

This equation represents the height of an object at time t when it is vertically thrown upwards or downwards and subject to gravitational acceleration.

To find the maximum height of the object, we can use the fact that the maximum point of a parabola occurs at its vertex. In this case, the vertex form of the equation is h(t) = -4.9(t - p)^2 + q, where (p, q) represents the coordinates of the vertex.

To determine the coordinates of the vertex, we need to find the values of p and q. The x-coordinate of the vertex, p, can be found using the formula p = -b / (2a), where a = -4.9 and b = 20. Substituting these values, we have p = -20 / (2 * -4.9) = 2.04.

To find the y-coordinate of the vertex, q, we substitute the value of t = 2.04 into the original equation h(t) = 20t - 4.9t^2. Evaluating this, we get h(2.04) = 20(2.04) - 4.9(2.04)^2 = 20.496 - 20.47584 = 0.02016.

Therefore, the vertex of the parabola is located at (2.04, 0.02016), representing the maximum height of the object.

Note: The negative coefficient (-4.9) on the t^2 term indicates that the parabola opens downwards, representing the object's initial upward motion and subsequent fall back towards the ground.