Question

two particles A and B travels along x and y axes with respective constant velocities V1 is I'm/s and V2 is 2j m/s.At time t=0 they are at position (-2,0) and (0,1) respectively.The position vector of particle B w.r.t to particle A at t=3 second will be?​

Answer 1

The position vector of particle B w.r.t to particle A at t=3 will be i - 7j

Explanation:

For Particle A travels along x and y axis:-

$x(0)=-2i$

$v(t)=i\ m/s$

Integrate w.r.t t

$x(t)=(t+c)i$

$x(0)=-2i$

Therefore, c = -2

$x_A(t) = (t-2)i$

$y_A(t)=0$

For Particle B travels along x and y axis:-

$x(0)=j$

$v(t)=2j\ m/s$

Integrate w.r.t t

$y(t)=(2t+c)j$

$y(0)=j$

Therefore, c = 1

$y_B(t) = (2t+1)j$

$x_B(t)=0$

• Position vector of particle A at t=3

$r_A(3)=i$

• Position vector of particle B at t=3

$r_B(t)=7j$

The position vector of particle B w.r.t to particle A at t=3

$r_{BA}=r_A-r_B$

$r_{BA}(3)=i-7j$

#Learn more:

A motor boat has a speed of 5 m/s. At time t=0, its position vector relative to a origin is(-11ỉ+16j) m, having the aim of getting as close as possible to a steamer. At time t=0, the steamer is at the point (4i +36j)m and is moving with constant velocity (10î-5j)m/s.

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Answer 2

The position vector of particle B w.r.t to particle A at t=3 second will be R(BA) = 7 j - 1 i = -1 i + 7 j

Explanation:

1. Here particle A and B at t=0 is (-2,0) and and (0,1).

2. Particle A is moving with 1(m/s) in positive i direction, So after 3 second new position of particle A

New position  = old position +  speed(v) × time(t)

A(t = 3) = -2i + (1 x 3 )i = +1i  .......(1)

3. Particle B is moving with 2(m/s) in positive j direction, So after 3 second new position of particle B

New position  = old position +  speed(v) × time(t)

B(t=3) = +1.j +(2 x 3) j = +7.j     .......(2)

4. Position vector of B with respect to A

R(BA) = B(t = 3) - A (t = 3)

Therefore,

R(BA) = 7 j - 1 i = -1 i + 7 j

Thus the position vector of particle B w.r.t to particle A at t=3 second will be R(BA) = 7 j - 1 i = -1 i + 7 j

Also learn more

The position vector of particle changes from 10 m  east to 10 m north in one second. What is the average  velocity of the particle?​

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