Question

Question #8df7c

Answer 1

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.