question_answer

Two cars are travelling towards a junction along two intersecting roads. One of them is 200 m away and is moving uniformly at 10 m/s. The other, located 100 m away, starts from rest and accelerates uniformly at \[\text{2 m}/{{\text{s}}^{\text{2}}}\]towards the junction. What is the interval between the moments when the cars pass the intersection?

Answer:

  Let O be the junction and AO and BO be the intersecting roads such that AO = 200 m and BO = 10 m To find the time interval \[\Delta t\]between the moments the cars pass the intersection point, we need to know time taken by the cars to reach the junction. If \[{{t}_{1}}\]and \[{{t}_{2}}\]are times taken by the two cars to reach the junction, then \[\Delta t=|{{t}_{2}}-{{t}_{1}}|\]                                         ….. (1) Let us find \[{{t}_{1}}\]and \[{{t}_{2}}\] OA \[{{S}_{1}}=200m\] \[{{u}_{1}}=10m/s\] \[{{t}_{1}}=?\] \[{{t}_{1}}=\frac{{{s}_{1}}}{{{u}_{1}}}=\frac{200}{10}=20s\] \[BO\] \[{{s}_{2}}=100m\] \[{{u}_{2}}=0\] \[{{a}_{2}}=2m/{{s}_{2}}\] \[{{t}_{2}}=?\] \[{{s}_{2}}={{u}_{2}}{{t}_{2}}+\frac{1}{2}{{a}_{2}}{{t}_{2}}\Rightarrow 100=\frac{1}{2}\times 2\times t_{2}^{2}\] \[\Rightarrow {{t}_{2}}=10\sec \] \[\therefore \Delta t={{t}_{1}}-{{t}_{2}}=20-10=10\sec .\] The interval between the moments when the cars pass the intersection is 10 sec.