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 f2 is an illustration of the three basic types of levers. Given that a = b = C = 1 and A = 3, B = 4,c = 4. What is the mechanical advantage of lever (1) and (2) respectively? Does lever (3) have a mechanical advantange or disadvantage?
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?
Suppose you want to send a rocket from the surface of the earth to a point 100 miles above the surface of the earth.
(a) What should be the initial velocity of the rocket?
(b) What should be the initial velocity (called the escape velocity) of the rocket for it to travel away from earth indefinitely and never return?
Motion above ground presents itself in various scenarios: motion upward, or downward and at various angles. Thanks to great thinkers like Galileo and Newton who laid solid foundational knowledge and Rene Descartes who invented the cartesian space in which much of the analyses is carried out.
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?