The ball is thrown vertically upwards from a height of 1.5 m with an initial speed of 1 m / s.

The ball is thrown vertically upwards from a height of 1.5 m with an initial speed of 1 m / s. The dependence of the height of the ball above the ground h (in m) on the flight time 1 (per second) is expressed by the formula h = -5t ^ 2 + 10t + 1.5. What is the maximum height the ball can climb?

Let us examine the function h (t) for extrema. To do this, we find its derivative:

h ‘= (-5t ^ 2 + 10t + 1.5)’ = -10t + 10.

Let us equate it to zero and find the inflection point:

-10t + 10 = 0;

-10t = -10;

t = 1.

The point t = 1 is the maximum point, we substitute its value into the height formula and find the value of the function:

h (1) = -5 * 1 ^ 2 + 10 * 1 + 1.5 = 6.5 m.

Answer: The maximum height of the ball from the ground is 6.5 m.