MATH6100 - CALCULUS 1 COURSE PROJECT Directions: Answer the following questions and show your complete and organized solutions 4. The sum of two positive numbers is 30. 1. A missile fired ground level rises x One of the numbers is multiplied by the meters vertically upwards in t seconds square of the other. If each number is and x = 50t - 6.2512. Find greater than 0, find the numbers that (i) the initial velocity of the missile, make this product a maximum. (i) the time when the height of the missile is a maximum (iii) the maximum height reached and 5. A wooden block is made as shown in (iv) the velocity with which the missile the diagram. The ends are right-angled strikes the ground triangles having sides 3x, 4x and 5x. The length of the block is y. The total surface 2. A particle of unit mass moves so that area of the block is 7,200 cm?. displacement after t seconds is given by x = 2 cos (1 - 2). Find the acceleration and kinetic energy at the end of 3 3T seconds. (K.E = (1/2) m v2) 3. The fuel used by a car is defined V by f(x)=3x2/80-6x+245, where x is the travelling speed in km/h. What is the most economical speed of the car? In other words, determine the speed of the car which uses the least amount of fuel