The diagram shows the start of a roller-coaster ride at a fairground.

Question

A car rises from A to B along a straight track.

( a ) AB = 80 meters and angle BAC = 18º.

Calculate the vertical height of B above A.

[ 2 ]

( b ) The car runs down the slope from B to D, a distance of s meters.

Use the formula s = t(p + qt) to find the magnitude of s, given that
p = 4, t = 3 and q = 3.8.

Answer 1

(a) To calculate the vertical height of B above A, we can use trigonometry.

sin(18°) = height/80
height = 80 * sin(18°)
height ≈ 28.87 meters

Therefore, the vertical height of B above A is approximately 28.87 meters.

(b) Substituting the given values into the formula s = t(p + qt):

s = 3(4 + 3.8*3)
s = 3(4 + 11.4)
s = 3(15.4)
s = 46.2

Therefore, the magnitude of s is 46.2 meters.