Help nursing student I can’t figure it out

Question

a volcano erupts, one piece of ash was ejected from the volcano with an initial velocity 368ft per/sec... The height is given with the equation H=-16t^2 +336t

We need to find out when does the ash projectile reach its maximum height. What is the maximum height. Last, when does the ash projectile reach the ground.

 

H=height in feet 

T= time in sec

This is a Parabola

Answer 1

We can identify the vertical speed from the equation - the coefficient of t is the vertical speed- 336. The actual speed is 368 ft/s. If we set the vertical height to zero, we can solve for t. T has two values - 0, the starting value, and 336/16 --> the landing time, which 21 seconds.

Since this is a parabola, the fling time is symmetrical around the maximum point. So the time at the maximum point is 21/2 - 10.5 seconds.

The maximum height is just the height equation, with t - 10.5 sec.