Question #8df7c

1 Answer
MetaPhysik
Jan 15, 2018

2.92 m/s

Explanation:

From distance and math concept.
The distance travels by Person 1 and Personal 2 are 2.5t and 1.5t respectively. These two distances form a right angle triangle, the distance between them is thus #sqrt((2.5t)^2+ (1.5t)^2)#, hence the rate of change is:

# sqrt((2.5t)^2+(1.5t)^2)/t= sqrt(2.5^2+1.5^2)= 2.92 m/s#

From relative velocity concept:

i) The velocity of Person 1 due East relative to Person 2 due South is:

#vec v_12 = vecv_1 - vecv_2 = 2.5 hati- (-1.5hatj) = 2.5 hati+1.5hatj #

#rArr v_12=|vec v_12| = sqrt(2.5^2+1.5^2)=2.92 m/s#

To Person 2 (going South), Person 1 is moving toward NE at 2.92 m/s

ii) The velocity of Person 2 relative to Person 1is:
#vec v_21 = vecv_2 - vecv_1 = -1.5 hatj-2.5hati = -2.5 hati-1.5hatj#
#rArr v_21 = sqrt(1.5^2+2.5^2) =2.92 m/s#

To Person 1 (going East), Person 2 is going SW at 2.92 m/s.

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