SOLUTION: hey there the question is- a cricket ball moves according to the rule d= 1 + 3/5x -1/50 x^2 where d is the height it rises after travelling x metrs horizontally ii) what

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Question 233536: hey there the question is-
a cricket ball moves according to the rule
d= 1 + 3/5x -1/50 x^2
where d is the height it rises after travelling x metrs horizontally

ii) what is the maximum height
iii)what is its original height
iv) if it was caught 2m above the ground, how far was it hit
thank you soo much for the help.
:)
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
a cricket ball moves according to the rule
d= 1 + 3/5x -1/50 x^2
where d is the height it rises after travelling x metrs horizontally
.
d= -1/50 x^2 + 3/5x + 1
.
ii) what is the maximum height
Since the coefficient associated with the x^2 term is negative, we know that it is a parabola that opens downwards. Finding the vertex gives you the maximum height.
x-axis of symmetry is at -b/2a
-b/2a = -(3/5)/(-2/50)
-b/2a = (3/5)/(1/25)
-b/2a = (3/5)(25/1)
-b/2a = (3/1)(5/1)
-b/2a = 15
To find the maximum height, plug it into:
d= -1/50 x^2 + 3/5x + 1
d= -1/50 (15)^2 + 3/5(15) + 1
d= -1/50 (225) + 45/5 + 1
d= -4.5 + 9 + 1
d = 5.5 meters
.
iii)what is its original height
Original height is when x=0
d= -1/50 x^2 + 3/5x + 1
d= -1/50 0^2 + 3/5(0) + 1
d= 1 meter
.
iv) if it was caught 2m above the ground, how far was it hit
Here, set d=0 and solve for x:
d= -1/50 x^2 + 3/5x + 1
2= -1/50 x^2 + 3/5x + 1.18
0= -1/50 x^2 + 3/5x - 2
Use the quadratic equation to solve for x doing so yields:
x = {3.82, 26.18}
We can throw out the 3.86 meters (too fast after being hit) leaving us with
x = 26 meters
.
(see details below)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.02x%5E2%2B0.6x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280.6%29%5E2-4%2A-0.02%2A-2=0.2.

Discriminant d=0.2 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.6%2B-sqrt%28+0.2+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.6%29%2Bsqrt%28+0.2+%29%29%2F2%5C-0.02+=+3.81966011250105
x%5B2%5D+=+%28-%280.6%29-sqrt%28+0.2+%29%29%2F2%5C-0.02+=+26.1803398874989

Quadratic expression -0.02x%5E2%2B0.6x%2B-2 can be factored:
-0.02x%5E2%2B0.6x%2B-2+=+-0.02%28x-3.81966011250105%29%2A%28x-26.1803398874989%29
Again, the answer is: 3.81966011250105, 26.1803398874989. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.02%2Ax%5E2%2B0.6%2Ax%2B-2+%29