Question

The equation $y = -16t^2 - 18t + 405$ describes the height (in feet) of a ball thrown downward at 18 feet per second from a height of 405 feet from the ground, as a function of time $t$, in seconds. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest tenth.

Answer 1

After 4.5 seconds the ball reaches ground.

Explanation:

We equation of motion given as y = -16t²-18t+405,

We need to find in how many seconds will the ball hit the ground,

That is we need to find time when y = 0

0 = -16t²-18t+405

16t²+18t-405 = 0

`t=(-18\pm √(18^2-4* 16* (-405)))/(2* 16)\\\\t=(-18\pm √(26244))/(32)\\\\t=(-18\pm 162)/(32)\\\\t=4.5s\texttt{ or }t=-5.625s`

Negative time is not possible, hence after 4.5 seconds the ball reaches ground.