Mathematics

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• Uphill and downhill
  The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?
• Gravitation
  From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
• Temperature change
  The mean temperature change is -3.2°F per day for five days. What is the total change over the five day period?
• Decorative fence
  The rectangular garden is 57 m long and 42 m wide. Calculate how much m² it will reduce if it encloses with a 60 cm wide decorative fence.
• Last page
  Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
• Four pavers
  Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
• Centroid - two bodies
  A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit

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