Question

A firework is launched from the top of a 92ft building with an initial upward velocity of 150ft/sec (equation = -16t^2 + vt + h).

When will the firework land if it doesn't explode?

A) t = 1.5 seconds.
B) t = 3.0 seconds.
C) t = 4.0 seconds.
D) t = 6.0 seconds.

Answer 1

The question asks for the time it takes for a firework launched from a building to land. We apply the quadratic formula to the motion equation, set the final height to zero, and solve for time 't'.

Step-by-step explanation:

The student is asking when a firework launched from a 92ft building with an initial upward velocity of 150ft/sec will land on the ground, considering it does not explode. The equation of the firework's vertical motion is -16t^2 + vt + h, where 'v' represents initial velocity, 'h' is the initial height, and 't' is the time in seconds. To determine when the firework will land, we need to solve for 't' when the height (h) is 0 (touchdown on the ground).

Using the given equation -16t^2 + 150t + 92 = 0 which represents the height, we set h to 0 and solve for 't'. After applying the quadratic formula, we find the positive value of 't' that indicates the time the firework takes to land.