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Question
A ball rolls down a slope and travels a distance d = t2 – 0.75t feet in t seconds. Find the time when the distance travelled by the ball is 11.25 feet
Solution
Distance = t2 – 0.75t
11.25 = t2 – 0.75t
Multiply by 100
1125 = 100t2 – 75t
100t2 – 75t – 1125 = 0 ...(Divided by 25)
4t2 – 3t – 45 = 0
a = 4,
b = – 3,
c = – 45
x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`
= `(3 ± sqrt(9 - 4(4)(- 45)))/8`
= `(3 ± sqrt(9 + 720))/8`
= `(3 ± sqrt(729))/8`
= `(3 ±27)/8`
= `(3 + 27)/8` or `(3 - 27)/8`
= `30/8` or `(-24)/8`
= `15/4` or – 3 ...(time will not be negative)
The required time = `15/4` seconds
= `3 3/4` second or 3.75 seconds
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