b) the height of the rocket when it is launched is found when t = 0
as found in part a, when t = 0, h = 0
therefore, height of rocket upon launch is 0m above the ground
c) the greatest height the rocket is given by the greatest h value shown in the graph, that is the h value of the turning point
greatest height reached by the rocket is 1575m above the ground
d) the time at which the rocket reaches its greatest height is given by the t value of the turning point
the rocket takes 25 seconds to reach the greatest height
e) the time that the rocket is in the air is given by doubling the answer to the previous question.
that is because the time it takes to reach its greatest height represents half the motion
the rocket on its way down will have the same distance to move, and therefore the same time as shown in the graph
therefore, the rocket is in the air for 50 seconds
2where x = length and y = width
a) the area of the paddock is given by length x width
therefore, A = xy
b) there perimeter of the new fence is given by the equation
P = 2(x + y)
P is known to be 40m
therefore, 2(x+y) = 40
x + y = 20
x = 20 - y
this describes the length
c) y = 20 - x
d) A = x(20 - x)
if wanted, answer can be written as A = 20x - x^2
e) find the x intercepts of the graph by letting A = 0
0 = x(20 - x)
x = 0 or 20 - x = 0
x = 0 or x = -20
the x coordinate of the turning point occurs half way between the two x intercepts
therefore, x value of turning point = -20/2 = -10
when x = -10
A = -10(20 + 10)
= -300
therefore, turning point occurs at (-10, -300)