vectors and kinematics

[Nupur]

hi,

here r some questions i'm unable to answer. plz help me

 

1. Two particles A and B are projected from the same point with equal angle theta = 30 degrees from the horizontal. If A has the projection velocity V_A = square root of 7 m/s and B has projection velocity V_B = 2*square root of 7 m/s. find the separation 'd' between them when their velocity vectors become mutually perpendicular to each other.

 

2. 2 intersecting straight lines move translationally in opposite directions with velocities v₁ and v₂ perpendiculr to the corresponding lines. the angle between the lines is alpha. find the speed of the point of intersection of these lines.

 

 

plzz post these solutions asap. thanks

nupur

[Tannin]

Question 2:

Draw two lines at the 90 degrees angle to each other. Now move only one line - the velocity of the point of the intersection, clearly, equals to the velocity of moving the line. If we move both lines, we get the point of intersection velocity as the hypotenuse of the right-angled triangle with the legs equal to the velocity of each line - use Pythagorean theorem. If initially the lines intersect at the angle alpha you should use the law of cosines (see Wikipedia - Triangle).

Question 1:

It is unclear from your problem, whether gravitation acts on the particles. If gravitation force does act on both particles remember the x-component of the velocity is conserved, and the y-component changes by -gt (where g is the free fall acceleration and t is the time passed). Create the scalar product of two vectors and make it equal zero (perpendicular) - from this condition you will be able to find the time by solving quadratic equation.

Good luck!