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

Answer 1

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