solutiones of exam

University of Babylon
College of Engineering
Mechanical Engineering Dept.
Mid-term Exam . Subject : Mathematics III
Max. Time: 1 hour.
Class : 2nd year - first semester.
Date: 30/ 11 / 2016
2016\ 2017 Max. mark : 15%

(Q1) / Find T , N , K and radius of curvature (?) of the curve

r (t) = ln ( t^2+1 ) i + (t - 2 tan^(-1)?t ) j at t = 2 .

(8 M.)
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(Q2) / { choose only two Branches } ( 7 M. )

((A)) Consider a 50-N weight suspended by two wires as shown in the figure . If the magnitude of vector F1 is 35 N , find angle ? and the magnitude of vector F2 .



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((B)) / Show that the curvature of a circle with center at the origin and radius a is ( 1/a ) ?

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((C)) / A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6 ft high net. It leave the point of impact with initial velocity of 35 ft /sec at an angle of 27 degree and slips by the opposing team untouched .

Find the vector equation for the path of the volleyball .
How high does the volleyball go , and when does it reach maximum height ?
Find its range and flight time .


Good Luck