a. Define scalar and vector physical quantities, and provide two examples of eac

Question

a. Define scalar and vector physical quantities, and provide two examples of each. b. The polar coordinates of a point are r = 7.5 m and theta = 205 degree. What are the Cartesian coordinates of this point? c. Find A B, |A + B|, and the direction of A = B if A = 5i - 3j and B = -3i-4 j d. After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of tie t is given by v(t) = 1.4 i -9.8t j. The balls displacement away from the edge of the table, during the time of 0.5 seconds for which the ball is in flight, is given by integral^0.5_0 v(t) dt. Calculate the displacement of the ball.

Explanation / Answer

According to the given probelm,

a) Scalar : A quantity with has no direction is called scalar Ex. 3, 6.7, 8.4, 22

Vector: A quantity with both magnitude and direction is called vector,

Ex. 3i+4j , 2i + 7j - 16k

b) Given polar coordinates, r = 7.5 and = 205o

is A = 7.5[cos205oi + sin205oj] = -6.8i - 3.17j

c) Given A = 5i - 3j and B = -3i -4j

A + B = (5 - 3)i + (-3 - 4)j = 2i - 7j

|A + B| = 22 + 72 = 7.28 units

d) Now, the dispalcement is given by,

X = 0.501.4i -9,8tj

X = [1.4t i - 9.8t2/2 j]0.50

X = 1.4[0.5-0]i - 4.9[0.52]j

X = 0.7 i - 1.225 j

X = 1.41m

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