Question

A ball is thrown straight up from a cliff. The function f(x) = –4.9t2 + 17t + 19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is that height reached? Round your answers to 1 decimal place.


Maximum height:

__ meters


Time:

__ seconds

Answer 1

Answer:

Maximum height: 33.7 meters

Time: 1.7 seconds

Step-by-step explanation:

Suppose we have a quadratic equation in the following format:

$f(t) = at^{2} + bt + c$

In a is negative, the maximum point of the function happens at the time of

$t_{v} = -\frac{b}{2a}$

And it's value is: $f(t_{v})$

In this question:

$f(t) = -4.9t^{2} + 17t + 19$

So $a = -4.9, b = 17, c = 19$

The time of the maximum height is:

$t_{v} = -\frac{b}{2a} = -\frac{17}{2*(-4.9)} = 1.7$

The maximum height is:

$f(1.7) = -4.9*(1.7)^{2} + 17*1.7 + 19 = 33.7$