✔ 最佳答案
In Figure ,ABCD is a rectangular inclined plane. E and F are points on the straight lines AB and CD respectively. F' is vertically below F. A, E, B and F' are on the same horizontal ground. ∠FAF' = 60° , ∠FEF' = 30° , ∠EFB = 20° and EF = 20m.
(a) Find
(1) FF' and AE
FF’= EF sin30 = 20 sin30
= 10cm
EF’= EF cos30 = 20 cos30
= 17.32cm
AF’ = FF’/tan60 = 10 / tan60
= 5.774cm
AE = √(AF’2 + EF’2) = √(5.7742 + 17.32’2)
= 18.26cm
(2) ∠AEF.
AF = FF’/sin60 = 10/sin60
= 11.55cm
cos∠AEF = (EF2 + AE2 – AF2) / (2AExEF) = (202 + 18.262 – 11.552) / (2x18.26x20)
∠AEF = 34.76o
(b) A small red toy car goes straight from E to B at an average speed of 2m/s while a small yellow toy car goes straight from F to B at an average speed of 3m/s. The two toy cars start going at the same time. Will the yellow toy car reach B before the red one ?
由F點沿斜面作一直線FE’平行AD及垂直於AB，EE’的長度等於AD
FE’ = AD = EFsin∠AEF = 20sin34.76 o
= 11.40cm
∠EFE’=90 - ∠AEF = 90 - 34.76 o
= 55.24o
EE’= FE cos∠AEF = 20cos34.76 o
=16.43cm
∠BFE’= ∠EFE’+ 20
= 75.24o
BE’ = FE’tan∠BFE’= 11.40tan75.24
= 43.30cm
BE = BE’-EE’ = 43.3 – 16.43 = 26.84cm
BF = FE’/cos∠BFE’= 11.40 / cos75.24
= 44.75cm
所以紅車需時
BE / 2 = 26.84/2
= 13.42s
黃車需時
BF / 3 = 44.75 / 3
= 14.92s
所以是黃車先到。
