Question

A ball is launched into the air from below a cliff, such that after t seconds its height above the cliff top is h metres, and is given by the equation

h=-4.9t²+19.6t -9.6
Calculate, to the nearest metre, the maximum height the ball achieves above the cliff top.

Answer 1

To determine the maximum height reached by the ball, calculate the time at which the ball reaches the maximum height using the vertex formula of a parabola, and then substitute this time back into the given quadratic equation.

Step-by-step explanation:

To find the maximum height above the cliff top achieved by the ball, we need to identify the vertex of the parabolic equation h=-4.9t²+19.6t-9.6. Since the equation is in the standard form h=at²+bt+c, where a, b, and c are constants, we can calculate the time at which the ball reaches its maximum height using the formula t=-b/(2a). Here, a=-4.9 and b=19.6, so the time at maximum height is t=-19.6/(2*(-4.9)).

Calculating, we get t=2 seconds. Substituting this back into the equation h=-4.9t²+19.6t-9.6 gives us the maximum height: h=-4.9*(2)²+19.6*(2)-9.6. After performing these calculations, the resulting height is rounded to the nearest metre, giving us the maximum height achieved by the ball above the cliff top.