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A ball is projected vertically upwards with an initial speed of 10 m s-1 at a height of 2.5m above the ground. In part (a) ignore all frictional forces.(a) (i) Draw a force diagram for the ball while it is in motion.
(ii) De?ne appropriate coordinate axes and an origin, and state the initial velocity and initial displacement in terms of the unit vectors and origin that you have chosen.
(iii) Determine, in terms of the magnitude of the acceleration due to gravity, g, the maximum height that the ball reaches above the point of projection, and the time taken to reach this position.
(iv) Determine the speed at which the ball hits the ground, correct to two decimal places, taking the value of g to be 9.81m s-2.
In the remainder of the question revise this model by taking air resistance into account. Model the ball as a sphere of diameter D and mass m, and assume that the quadratic model of air resistance applies.
Sketch a graph of the given function C(h) - Where is the vertical asymptote? Does it play a role in this context?
Find the slope of the line that passes through the points (3, -5) and (-4, -6). Find the equation in slope-intercept form, of the line that passes through the points (3, 6) and (-7, -3); write equation in slope-intercept form.
Give five interesting facts about group theory (or tensor calculus). Each one need only be 1 to just a few sentences - please list separately and under each fact provide any links to websites or pictures etc.
Find the volume of a triangle with sides y = 2, y = x+1, y = 11-x. The vertices are (5, 6), (1, 2) and (9, 2). Find the volume by rotating about y-axis:
Consider the curve 5x3+8xy+5y2 = 45. Use implicit differentiation to calculate the derivative dy/dx. Hence determine the point/s which has/have a horizontal tangent.
Suppose that at a certain instant the volume is 590 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 13 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
The perimeter of a rectangular lot is 56 meters. The length exceeds the width by 12 meters. Find the length of the lot.
suppose the position of a particle after t seconds is given by the following vector equationft 1 cos2pit sin2pitat t
compare and contrast the gaussian elimination method with the gauss-jordan method of solving a system of linear
find the dimensions of the poster with the smallest area. Note: The answer to this problem requires that you enter the correct units.
Find the area of the region bounded by 2 curves.
able industries bought a fax machine for $250. it is expected to depreciate at a rate of 25% per year. what will the value of the fax machine be in 3 years?
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