Question

The path of a firework is described by the function: h(1) = 4.97? + 491 + 1.5
where h(t) is the height of the firework, in meters, and t is the time in seconds since the launch.
a) Sketch the pathway of the firework,
b) Determine the maximum height of the firework.

Answer 1

a) To sketch the pathway of the firework, we need to plot the function h(t) on a coordinate plane.

First, we can notice that 4.97? + 491 + 1.5 is just a constant value of approximately 497.5. So we can rewrite the function as:

h(t) = 497.5

This means that the height of the firework is constant at 497.5 meters for the entire time it is in the air. Therefore, the pathway of the firework is a straight horizontal line at a height of 497.5 meters.

b) The maximum height of the firework is 497.5 meters, as shown in part a.