Question:
A body is thrown vertically upward. The height ,h, attained in time ,t , is given by h=20t-49/10t^2. I do not know to determine the maximum height reached by the body.

There are 3 methods you can use to find the maximum height. One way is to use the formula for vertex of a parabola. Another way is to find the roots of the parabola, then take the average. The third way is to use calculus to take the derivative and set it to 0. Each of these methods will give the time the body reaches the maximum height, which we can plug into the original equation to find the value of h.

Method 1: Vertex of a parabola

For a parabola y = ax² + bx + c, the vertex is at x = -b / 2a. In this case, a = -4.9 and b = 20.

x = -b / 2a

x = -20 / (2 × -4.9)

x = 2.04

The body reaches the maximum height after 2.04 seconds. This corresponds to a height of:

h = 20 (2.04) − 4.9 (2.04)²

h = 20.4 meters

Method 2: Roots of a parabola

For any parabola, the vertex is halfway between the roots, or zeros.

h = 20t − 4.9t²

h = t (20 − 4.9 t)

0 = t (20 − 4.9 t)

t = 0 or 4.08

The vertex is therefore at t = (0 + 4.08) / 2 = 2.04 seconds. As found earlier, this corresponds to a height of 20.4 meters.

Method 3: Calculus

The maximum is found where the first derivative is 0.

h = 20t − 4.9t²

dh/dt = 20 − 9.8t

0 = 20 − 9.8t

t = 2.04

Again, the height is 20.4 meters.

Question: A body is thrown vertically upward. The height ,h, attained in time ,t , is given by h=20t-49/10t^2. I do not know to determine the maximum height reached by the body.

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Question:
A body is thrown vertically upward. The height ,h, attained in time ,t , is given by h=20t-49/10t^2. I do not know to determine the maximum height reached by the body.