question_answer

Particle A moves along the line \[y=4\sqrt{3}\,m\] with constant velocity v of magnitude 2.0 m/s and directed parallel to the positive re-axis (see figure). Particle B starts at the origin with zero speed and constant accelerationa (of magnitude \[4.0\,m/{{s}^{2}}\]) at the same instant that the particle A passes the y axis. The angle \[\theta \] between a and the positive y axis that would result in a collision between these two particles should have a value equal to

A)  \[{{30}^{o}}\]                                   

B)  \[{{45}^{o}}\]

C)  \[{{50}^{o}}\]                  

D)  \[{{60}^{o}}\]

Correct Answer: A

Solution :

                Given that \[y=4\sqrt{3}\,m\] For particle A, v = 2 m/s and For particle B \[a=4\,m/{{s}^{2}}\] Let particle are collide after t sec. distance covered by A in \[t\sec .=2\,t\] and B,   \[=\frac{1}{2}\times 4\times {{t}^{2}}\]                 For collision                 \[2t=\frac{1}{2}\times 4\times {{t}^{2}}\]                 \[t=1\,\sec \]. Velocity of \[B=4\times 1=4\,m/s\] Now, from MBC                                 \[\sin \theta =\frac{2}{4}=\frac{1}{2}\]                                 \[\theta ={{30}^{o}}\]