Question

A fireworks mortar is launched straight upward from a pool deck platform 6 m off the ground at an initial velocity of 48 m/sec. The height of the mortar can be modeled by h(t)=−4.9t2+48t−6, where h(t) is the height in meters and t is the time in seconds after launch. What is the maximum height? Round to the nearest meter.

A) 199 m
B) 5 m
C) 6 m
D) 124 m

Answer 1

The maximum height of the fireworks mortar is approximately 112 meters.

Step-by-step explanation:

To determine the maximum height of the fireworks mortar, we need to find the vertex of the quadratic equation representing the height. The equation h(t) = -4.9t^2 + 48t - 6 is in the form h(t) = at^2 + bt + c, where a = -4.9, b = 48, and c = -6. The vertex of a quadratic equation in the form h(t) = at^2 + bt + c is given by the formula t = -b/(2a). Plugging in the values, we get t = -48/(2*(-4.9)) = 4.9 seconds. To find the maximum height, we substitute this value of t back into the equation h(t) = -4.9t^2 + 48t - 6.

h(4.9) = -4.9*(4.9)^2 + 48*(4.9) - 6 = -4.9*24.01 + 235.2 - 6 = -117.449 + 229.2 = 111.751.

Therefore, the maximum height of the fireworks mortar is approximately 112 meters.