Answer to Question #226550 in Mechanics | Relativity for sdfsef

Question

Lean and Mickey who are 150 m apart start walking toward each other at 3 m/s and 5 m/s respectively.a. How long will it take them to meeteach?b. Find the corresponding distance traveled by each ?​

Answer 1

a)

$d = 150\text{ m}; v_1 = 3.0\frac{\text{m}}{\text{s}}; v_2 = 5.0\frac{\text{m}}{\text{s}}.$

Relative speed of one object to the other, since they are moving towards each other, will be (imagine it as speed of one object in the reference frame of the other being stationery therein):

$v = v_1 + v_2.$

Time passed until meeting (all distance covered):

$t = \frac{d}{v} = \frac{d}{v_1+v_2} = \frac{150\text{ m}}{3.0\frac{\text{m}}{\text{s}} + 5.0\frac{\text{m}}{\text{s}}} = 18.75\text{ s}.$

b)Distances traveled by each object respectively:

$d_1 = v_1t = \frac{v_1}{v_1+v_2}d = \frac{3.0\frac{\text{m}}{\text{s}}}{3.0\frac{\text{m}}{\text{s}} + 5.0\frac{\text{m}}{\text{s}}}150\text{ m} = 56.25\text{ m}; \\ d_2 = v_2t = \frac{v_2}{v_1+v_2}d = \frac{5.0\frac{\text{m}}{\text{s}}}{3.0\frac{\text{m}}{\text{s}} + 5.0\frac{\text{m}}{\text{s}}}150\text{ m} = 93.75\text{ m}.$