what is the maximum height the ball reaches? how long will it take the baseball to reach the maximum height? how long does it take for it to reach the ground?

Question

a baseball player hit a ball with an upward velocity of 46ft/s. its height h in feet after t seconds is given by the function h=-16t² +46t+6

Answer 1

h=-16t^2+46t+6

divide all be -2

 

8t^2-23t-3=h

factors 8*1 and 3*1

(8t+1)(t-3)

t=-1/8, t=3

time 3 seconds

 

vertex formula

-b/2a

46=b, -b therefore is -46

-16=a

-46/2(-16)= 1.44secs

substitute for the value of t

 

-16(1.44)^2+46(1.44)+6=h

-16(2.07)+66.24+6=h

-33.18+66.24+6=h

39.06=h

 

Answer 2

The function is quadratic, which means that when plotting height vs. time a parabola is the graph.  The maximum height will occur at the vertex of the parabola.  We can find that maximum height by first finding the amount of time it takes to reach that height, then plug that time into the height function.  To find the value of t we know it will occur at -b/(2a). 

That gives us t =-46/(2*(-16)) = 1.4375 seconds.  plugging this time into the function gives us:

 

h=-16(1.4375)² + 46(1.4375) + 6 = 58.191 feet.