Position Vector

Q.

A watermelon seed has the following coordinates: x=-5.0 m, y=9.0 m and z=0 m. Find its position vector

(a) In unit-vector notation and as
(b) A magnitude and
(c) An angle relative to the positive direction of the x-axis

1. $Insufficientdata$

2. $-5\hat{i}+9\hat{j},\sqrt{106},si{n}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$

3. $-5\hat{i}+9\hat{k},\sqrt{106},co{s}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$

4. $-5\hat{i}+9\hat{j},\sqrt{106},co{s}^{-1}\left(\frac{-5}{\sqrt{106}}\right)$

Q. Two cars $A$ and $B$ move on a straight road with constant velocity. When they move in same direction, they come close by $8\text{m}$ in $10\text{s}$ and when they move in opposite direction towards each other, they come close by $20\text{m in 1 s}$. The speed of the cars A and B (in $m/s$) respectively are

1. $9.6\text{and}10.4$
2. $10.4\text{and}9.6$
3. $20.8\text{and}10.4$
4. $10.4\text{and}20.8$

Q. The position vector of point B (8, 4) with respect to point A (3, 7) is

1. 8i + 4j
2. 3i + 7j
3. 11i + 11j
4. 5i – 3j

Q. Ship $A$ is sailing towards north-east with velocity $\overrightarrow{v}=30\hat{i}+50\hat{j}km/h$, where $\hat{i}$ points east and $\hat{j}$ points north. Ship $B$ at a distance of $80km$ east and $150km$ north of ship $A$ is sailing towards the west at $10km/h$. $A$ will be at minimum distance from $B$ in

1. $4.2h$
2. $2.6h$
3. $3.2h$
4. $2.2h$

Q. At time $t=0\text{s}$, a particle starts from rest at position $(4\text{m},8\text{m})$. It starts moving towards the positive $x$-axis with a constant acceleration of $2{\text{m/s}}^2$. After $2\text{s}$, it undergoes an additional acceleration of $4{\text{m/s}}^2$ in the positive $y$-direction. Find the coordinates of the particle (in $\text{m}$) after the next $5\text{s}$.

1. $(58,6)$
2. $(53,58)$
3. $(-53,58)$
4. $(58,-6)$

Q. Two cars $A$ and $B$ move on a straight road with constant velocity. When they move in same direction, they come close by $8\text{m}$ in $10\text{s}$ and when they move in opposite direction towards each other, they come close by $20\text{m in 1 s}$. The speed of the cars A and B (in $m/s$) respectively are

1. $9.6\text{and}10.4$
2. $10.4\text{and}9.6$
3. $20.8\text{and}10.4$
4. $10.4\text{and}20.8$

Q.

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates(meters) of the rabbit's position as function of time t(seconds) are given by

$x\left(t\right)=-\frac{t^2}{2}+5t+20Andy\left(t\right)=t^2-10t+30$

(a)At t=10s, what is the rabbot's position vector $\overrightarrow{r}$ in unit-vector notation and in magnitude-angle notation?

1. $20\hat{i}-30\hat{j};20\sqrt{13}\&ta{n}^{-1}\left(\frac{3}{2}\right)$

2. $30\hat{i}-20\hat{j};10\sqrt{13}\&ta{n}^{-1}\left(\frac{-2}{3}\right)$

3. $20\hat{i}+30\hat{j};10\sqrt{13}\&ta{n}^{-1}\left(\frac{3}{2}\right)$

4. $30\hat{i}+20\hat{j};10\sqrt{3}\&ta{n}^{-1}\left(\frac{2}{3}\right)$

Q. A bird moves from point $A$ $(1,-2,3)$ to $B$ $(4,2,3)$. If the speed of the bird is $10\text{m/s}$, then the velocity vector of the bird is:

1. $5(\hat{i}-2\hat{j}+3\hat{k})\text{m/s}$
2. $5(4\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$
3. $(0.6\hat{i}+0.8\hat{j})\text{m/s}$
4. $(6\hat{i}+8\hat{j})\text{m/s}$