Question

i don't understand any of this /: please help
equation: h = -16t^2 + 58t + 3 where h is feet of a baseball after t seconds after it has been hit

find the initial height of the ball when it makes contact with the bat

after how many seconds was the baseball 40ft above the ground?

when was the ball 60 ft above the ground?

when will the ball hit the ground?

when does the ball reach its maximum height?

what was the maximum height of the ball?

state the domain

Answer 1

>>> find the initial height of the ball when it makes contact with the bat

simply put t=0 in the given equation

Answer 2

here h (height ) is given to be function of t (time )
see initially t=0
plug in t=0 in h = -16t^2 + 58t + 3 to get the initial height

Answer 3

after putting t=0 here u will get h=3 (the required height)

Answer 4

after how many seconds was the baseball 40ft above the ground?

here h=+40 u need to find the time t

Answer 5

thus h = -16t^2 + 58t + 3
so we have 40=-16t^2 + 58t + 3
or
16t^2 -58t +37=0 just solve for t (the least positive value of t is the required answer)

Answer 6

when was the ball 60 ft above the ground?
here again h=60 u need to find t

Answer 7

when will the ball hit the ground?
again here u have to find t when h=0

Answer 8

find first derivative wrt t of
h = -16t^2 + 58t + 3
thus dh/dt = -32t +58

at max height dh/dt =0 (in other words the ball momentarily comes to rest just before coming down)
so time of ascent t=58/32

Answer 9

find h after plugging t=58/32

Answer 10

thank you so much (:

Answer 11

welcome dear ...