Hw02: Problem 12 Previous Problem List Next (1 point) The height y (n feet) of a

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Hw02: Problem 12 Previous Problem List Next (1 point) The height y (n feet) of a ball thrown by a child is 14 where r is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? 5 feet feet (b) What is the maximum height of the ball? 17 (c) How far from the child does the ball strike the ground? 2.78 Note: Your answer for part (c) needs to be correct up to two decimal points. feet Note: You can You have attempted this problem 8 times Your overall recorded score is 67%. You have 17 attempts remaining

Explanation / Answer

We have given the height of a ball is y=(-1/14)x2+2x+5 in feet

a) when the ball leaves the child hand,the horizontal distance is 0

therefore x=0

substitute x=0 into y

y=(-1/14)(0)2+2(0)+5=5

y=5

therefore the ball is 5 feet when it leaves the child's hand

b) change the equation into vertex form y=a(x-h)2+k by completing the square.

y=(-1/14)x2+2x+5

y=(-1/14)(x2-28x)+5

y=(-1/14)(x2-28x+196-196)+5

y=(-1/14)(x2-28x+196)+(1/14)*196+5

y=(-1/14)(x-14)2+14+5

y=(-1/14)(x-14)2+19

the maximum height of the ball is 19 feet

c) when the ball hits the ground y=0

y=(-1/14)x2+2x+5=0

(-1/14)x2+2x+5=0

use the quadratic formula to find x

x=[-b(+or -)sqrt(b2-4ac)]/2a

we have a=-1/14,b=2,c=5

x=[-2(+or -)sqrt(4-4(-1/14)*5)]/(2(-1/14))

x=[-2(+or -)sqrt(4+10/7)]/(-1/7)

x=[-2(+or -)sqrt(38/7)]/(-1/7)

x=[-2+sqrt(38/7)]/(-1/7),x=[-2-sqrt(38/7)]/(-1/7)

x=-2.3095064303,x=30.3095064303

the ball is 30.31 feet from the child when it strikes the ground.

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