Answer :
Answer:
20.4 meters
Explanation:
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.
