Dido, The mathematician. She was an ancient queen of Carthage. If she never existed, our world would have been totally different, for example, the progenitors of the founders of Rome would have been different. Maybe Rome would even not have been founded.
Figure m5 is an illustration of a projectile, say a shell fired with an initial velocity of V ft/sec from a cannon inclined at an angle of θ to the ground. Now suppose a shell is fired from a cannon inclined at an angle of 45 degrees with the ground and the shell is given an initial velocity of 2000 ft/sec.
(a) What are the horizontal and vertical velocities of the shell?
(b) Determine the parametric equations of the motion of the shell.
(c) Find the range of the shell.
(d) What is the maximum height above ground attained by the shell during its flight?
A bomb is released from an airplane which is flying horizontally at a speed of 240 mph.
(a) Determine the parametric equations of motion of the bomb.
(b) How long will it take the bomb to strike the ground if the airplane is flying at 1 mile above ground?
(c) How long will it take the bomb to strike the ground if the speed of the airplane is 300 mph instead of 240?
(d) How long will it take the bomb to strike the ground if the airplane is flying at 2 miles above ground and at 240 mph?
(e) What is the horizontal distance between the point where the bomb strikes the ground and the point on the ground directly below the point at which the bomb is released?
A farmer has 100ft of fencing which he wants to use to enclose the rectangular area ABCD, and to partition the rectangle into two equal rectangles (fig 1). What should be the dimensions of the rectangle ABCD, if he wants to enclose the maximum total area?
Space equilibrium is a basic desire of all entities. Yet many politicians are either unfamiliar with or refusing to adhere to the fundamental law of space governance. Any entity that occupies any space without consent, must be prepared for opposition by owners of the space. Even when there is total conquest, the desire to repossess ownership always exists among owners of the conquered space. Inadherence to the fundamental law of space is the chief reason for chaos in many spaces of the world.