SUPPLEMENTARY PROBLEMS
A 50 l b block of ice is on a ramp inclined at
20^{0}. What force pushing up the ramp is required
to keep the block from sliding? What is the actual force caused by the weight of ice against the
ramp? Ans. 171 l b and 47 l b
A man can row his boat at 3 mph. He is in a steam flowing from north to south at 4 mph. How
fast and in what direction will he travel if rows i) directly downstream ii) directly upstream iii) due
east (across the stream) iv) North East (45^{0} on a navigator campass)
Ans i) 7mph.s ii)1 mph.s iii) 5 mph;
143.130^{0} iv) 2.8336 mph; 131.529^{0}
A petrol boat leaves its base on a heading of
17^{0 }travelling at 17 km/hr. After 2 hours it turns
to new heading of 310^{0} and slows to 12 km/hr after 45 minutes on this new heading. How far and
in what direction is the boat from its base. Ans. 38.420 km, 4.5476^{0}
A manual lawnmover requires a force of 10 lbs parallel to the ground in order to move it through
the grass; if the handle is inclined at 41^{0} to the ground. How much force is necessary along the handle?
Ans. 13.2501 l bs
In a plane add 120 N Force at 30^{0} and a 100 N force at 90^{0} using the parallelogram method.
Ans. R= 11/N , q = 339^{0} with
Plot the points with the given polar coordinates
(i) (1, 18^{0} ) (ii) (2.3, 400) (iii) (1,
7p /6 rad) (iv) (5, 5rad)
Ans.
Find the set of polar coordinates for the points with given Cartesian coordinates.
(i) (3, 0) (ii) (2, 2Ö3) (iii) (5, 12) (iv) ( 1, 3)
Ans. i) (3, 180^{0}) (ii) (4, 60^{0}) (iii) (13,
67.38^{0} (iv) ( Ö10, 71.57^{0})
Convert the equations to polar form (i) x = 7 (ii) x^{2}+ y^{2} = 9 (iii) y = 2x (iv) x^{2} y^{2} = 1 (v)
Ans. (i) r cos q =7 (ii) r = 3 (iii) q = tan1 (2) (iv) r^{2} cos 2q = 1 (v) r^{2} (cos^{2} q + 4 sin^{2} q ) = 4
Convert the equations to Cartesian coordinates
(i) r = 3 (ii) q = 3p/4 (iii) r sin
q =7 (iv) r^{2} cos q = 3 sin q  cos q
Ans. (i) x^{2} + y^{2} = 9 (ii) y = x (iii) y = 7 (iv) (x^{2} + y^{2} ) x = 3y x
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Index
7.1 Scalers & Vectors 7.2 Algebra of Vectors 7.3 Representation of a vector in a plane 7.4 Dotor Scalar product 7.5 Polar Coordinates Supplementary Problems
Chapter 8
