This mathematical series of puzzle caches has questions from all levels of school education, from Key Stage 1 (age 5-7) in the first few caches, all the way up to Further Maths A-Level in the last few caches. Everybody should be able to get the solutions to the first few caches, but how far through the series will you be able to get? For a full description of the series, please see the first cache “1+1=1”. If you can’t solve a particular set of questions, try asking somebody of the appropriate age, or your friendly neighbourhood Maths teacher!
Please note that many of the caches are hidden near busy roads, so please take care when finding them, especially if you have children with you. It is worth noting that there is parking possible within a few hundred metres of all caches and a quick look on a satellite view map should show suitable places.
This cache contains questions from the A-Level Further Maths course, from the Mechanics modules.
1. A geocacher on the hunt for a First To Find moves along a straight line of bushes, such that their velocity v m/s, given in terms of time t seconds, is v=(1/2)t^2 – 3t +4. A= the total distance traveled between t=0 and t=4, in metres.
2. Two particles, G and H, of masses 2m and m, are on a smooth horizontal table. H is at rest and G collides with it when it is moving with speed u. After the collision, the total kinetic energy of the two particles is (3/4) m*u^2 (where * means multiply). The coefficient of restitution between the two particles is 1/B. Find B.
3. A hollow right circular cone, with base of radius r and height h, is fixed with its axis vertical and vertex downwards. A particle moves with constant speed v in a horizontal circle of radius (1/3)*r on the smooth inner surface of the cone. V=sqrt(h*g/C), where sqrt means square root. Find C.
4. A particle of mass 4kg is moving along the horizontal x-axis under the action of a single force which acts in the positive x-direction. At time t seconds, the force has magnitude (1+3t^(1/2))N. When t=0, the particle has speed 2m/s in the positive x-direction. D=the work done by the force in the interval from t=0 to t=4, written to one significant figure. Find D.
5. A light elastic string has natural length 10m and modulus of elasticity 130N. The ends of the string are attached to fixed points P and Q, which are at the same horizontal level and 12.6m apart. An object is attached to the midpoint of the string and hangs in equilibrium at a point 1.6m below PQ. Find E, the weight of the object, to 2 significant figures.
The cache can be found at N50 45.PQR E0 13.STU where P=A+B, Q=C, R=E-2A-C, S=D-18C-17A+20B, T=D-4E-9, U=B+C
You can check your answers for this puzzle on GeoChecker.com.