Relative Motion in Two Dimensions
PHXI04:MOTION IN A PLANE

362098 A bird is flying with a speed of 40 \(km\)/\(hr\) in north direction. A train is moving with a speed of 40 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
2 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
3 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
4 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362099 A bird is flying with a speed of 20 \(km\)/\(hr\) in north direction. A train is moving with a speed of 20 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
2 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
3 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
4 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362100 Let \(\vec{r}_{1}(t)=3 t \hat{i}+4 t^{2} \hat{j}\) and \(\vec{r}_{2}(t)=4 t^{2} \hat{i}+3 t \hat{j}\) represent the positions of particles 1 and 2 respectively as function of time \(t ; \vec{r}_{1}(t)\) and \(\vec{r}_{2}(t)\) are in \(m\) and \(t\) in \(s\). The relative speed of the two particles at the instant \(t=1 s\), will be

1 \(1\;\,m{s^{ - 1}}\)
2 \(3\sqrt 2 \;\,m{s^{ - 1}}\)
3 \(5\sqrt 2 \;\,m{s^{ - 1}}\)
4 \(7\sqrt 2 \;\,m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE

362101 A flag is mounted on a car moving due North with velocity of 20 \(km\)/\(hr\). Strong winds are blowing due East with velocity of 20 \(km\)/\(hr\). The flag will point in direction

1 East
2 North - East
3 South - East
4 South - West
PHXI04:MOTION IN A PLANE

362098 A bird is flying with a speed of 40 \(km\)/\(hr\) in north direction. A train is moving with a speed of 40 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
2 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
3 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
4 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362099 A bird is flying with a speed of 20 \(km\)/\(hr\) in north direction. A train is moving with a speed of 20 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
2 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
3 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
4 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362100 Let \(\vec{r}_{1}(t)=3 t \hat{i}+4 t^{2} \hat{j}\) and \(\vec{r}_{2}(t)=4 t^{2} \hat{i}+3 t \hat{j}\) represent the positions of particles 1 and 2 respectively as function of time \(t ; \vec{r}_{1}(t)\) and \(\vec{r}_{2}(t)\) are in \(m\) and \(t\) in \(s\). The relative speed of the two particles at the instant \(t=1 s\), will be

1 \(1\;\,m{s^{ - 1}}\)
2 \(3\sqrt 2 \;\,m{s^{ - 1}}\)
3 \(5\sqrt 2 \;\,m{s^{ - 1}}\)
4 \(7\sqrt 2 \;\,m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE

362101 A flag is mounted on a car moving due North with velocity of 20 \(km\)/\(hr\). Strong winds are blowing due East with velocity of 20 \(km\)/\(hr\). The flag will point in direction

1 East
2 North - East
3 South - East
4 South - West
PHXI04:MOTION IN A PLANE

362098 A bird is flying with a speed of 40 \(km\)/\(hr\) in north direction. A train is moving with a speed of 40 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
2 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
3 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
4 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362099 A bird is flying with a speed of 20 \(km\)/\(hr\) in north direction. A train is moving with a speed of 20 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
2 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
3 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
4 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362100 Let \(\vec{r}_{1}(t)=3 t \hat{i}+4 t^{2} \hat{j}\) and \(\vec{r}_{2}(t)=4 t^{2} \hat{i}+3 t \hat{j}\) represent the positions of particles 1 and 2 respectively as function of time \(t ; \vec{r}_{1}(t)\) and \(\vec{r}_{2}(t)\) are in \(m\) and \(t\) in \(s\). The relative speed of the two particles at the instant \(t=1 s\), will be

1 \(1\;\,m{s^{ - 1}}\)
2 \(3\sqrt 2 \;\,m{s^{ - 1}}\)
3 \(5\sqrt 2 \;\,m{s^{ - 1}}\)
4 \(7\sqrt 2 \;\,m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE

362101 A flag is mounted on a car moving due North with velocity of 20 \(km\)/\(hr\). Strong winds are blowing due East with velocity of 20 \(km\)/\(hr\). The flag will point in direction

1 East
2 North - East
3 South - East
4 South - West
PHXI04:MOTION IN A PLANE

362098 A bird is flying with a speed of 40 \(km\)/\(hr\) in north direction. A train is moving with a speed of 40 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
2 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,\,{\mathop{\rm direction}\nolimits} \)
3 \(40\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
4 \(40\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362099 A bird is flying with a speed of 20 \(km\)/\(hr\) in north direction. A train is moving with a speed of 20 \(km\)/\(hr\) in west direction. A passenger sitting in the train will see the bird moving with velocity.

1 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
2 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NE\,{\mathop{\rm direction}\nolimits} \)
3 \(20\sqrt 2 \,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
4 \(20\,km/hr{\mkern 1mu} \,in{\mkern 1mu} NW\,{\mathop{\rm direction}\nolimits} \)
PHXI04:MOTION IN A PLANE

362100 Let \(\vec{r}_{1}(t)=3 t \hat{i}+4 t^{2} \hat{j}\) and \(\vec{r}_{2}(t)=4 t^{2} \hat{i}+3 t \hat{j}\) represent the positions of particles 1 and 2 respectively as function of time \(t ; \vec{r}_{1}(t)\) and \(\vec{r}_{2}(t)\) are in \(m\) and \(t\) in \(s\). The relative speed of the two particles at the instant \(t=1 s\), will be

1 \(1\;\,m{s^{ - 1}}\)
2 \(3\sqrt 2 \;\,m{s^{ - 1}}\)
3 \(5\sqrt 2 \;\,m{s^{ - 1}}\)
4 \(7\sqrt 2 \;\,m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE

362101 A flag is mounted on a car moving due North with velocity of 20 \(km\)/\(hr\). Strong winds are blowing due East with velocity of 20 \(km\)/\(hr\). The flag will point in direction

1 East
2 North - East
3 South - East
4 South - West