Question

The equation for a projectile's height versus time is h(t) = -16+2 +Vot+to. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height? Round to the nearest hundredth.

Answer 1

Given the equation of a projectile to be:

$h(t)=-16t^2+v_0t+h_0$

Initial height = 2 feet

Initial speed = 110 feet per second.

That is,

$h_0=2,v_0=110\text{ f}eet\text{ per second}$

Substitute the initial height and speed into the projectile equation,

$h(t)=-16t^2+110t+2$

The graph of the projectile is shown below:

From the graph, the time it takes the ball to attain maximum height to the nearest hundredth is 3.44 seconds