A body is projected vertically upward and the height hmeters reached after a time t seconds is given by h=196t-4.9t^2.find the time taken to reach the greatest height and the greatest height reached

Answer 1

To find the time taken to reach the greatest height, we need to find the vertex of the equation h = 196t - 4.9t^2.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the x-coordinate: x = -b/2a.

In this case, the equation is h = -4.9t^2 + 196t.
Comparing this to the general form y = ax^2 + bx + c, we have:
a = -4.9
b = 196

Using the formula for the x-coordinate of the vertex, we calculate:
t = -196 / (2*(-4.9))
t = -196 / -9.8
t = 20

So, the time taken to reach the greatest height is 20 seconds.

To find the greatest height reached, we substitute this time back into the equation:
h = 196(20) - 4.9(20)^2
h = 3920 - 4.9(400)
h = 3920 - 1960
h = 1960

Therefore, the greatest height reached is 1960 meters.