By R. Haines;B. Haines
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Extra resources for Work Out Applied Mathematics: ‘A’ Level
6 An aircraft A is travelling due west at 240 mile h- 1 • At noon a second aircraft B, at the same altitude, is 40 miles away from A in a southwesterly direction. One hour later B is again 40 miles away but now in a north-westerly direction. Calculate the position vector of B relative to A at time t. Deduce the minimum distance between A and B and show that this is when B is due west of A. Find the velocity of B. 2. 7 In this question distances are measured in metres and time in seconds. At time t = 0 two particles P and Q are set in motion in the x-y plane.
9 . TO resultant of W and => cos2 MY NY' cos()=-- cos2 () __ = _ _W 2 (w + W) w Alternatively, take moments about N. Length of string=~ = 2a cos() J (b) Taking moments about X: T = 2w + W = 2 sin() j( 2 (w + W W)) . 6 Taking moments about A: T(2a sin 20) = Wa cosO+ W (2a cosO), T= 3W . 4sin0 y 8 A Resolving, X = T cos e = 3 W 4cot e , . R =W ReactiOn - y(9 cot 2 4 Y =2W - e + 25) at tan- 1 -yX = tan= If R is perpendicular to BC, if>= AC= 2(2asin0) => T sin e, so tan e =t. e = ~4 W. 1 (3 cot5 e) if> to the vertical.
3 Systems of Coplanar Forces. Frameworks Forces as vectors. Composition and resolution of coplanar forces. Resultant of coplanar forces. Triangle and polygon of forces. Moment of a force about a point. ) Couples. Reduction of a coplanar system of forces to a force at a point and a couple. Problems may require clear force diagrams. Graphical solutions may be permitted where appropriate. 1 Fact Sheet (a) Definitions (i) The component of a force F, having magnitude F, in a direction making 0 with F is F cos 0.
Work Out Applied Mathematics: ‘A’ Level by R. Haines;B. Haines