A shell is fired at a speed of 200 m/s at an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the tower be at the origin $(0, 80)$. The initial velocity of shell $1$ is $\vec{v}_1 = 200(\cos 37^o \hat{i} + \sin 37^o \hat{j}) = 200(0.8 \

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the tower be at the origin $(0, 80)$. The initial velocity of shell $1$ is $\vec{v}_1 = 200(\cos 37^o \hat{i} + \sin 37^o \hat{j}) = 200(0.8 \hat{i} + 0.6 \hat{j}) = 160 \hat{i} + 120 \hat{j}\ m/s$.The jeep moves with $\vec{v}_J = 10 \hat{i}\ m/s$. The velocity of shell $2$ relative to the jeep is $\vec{v}_{2J} = 250(\cos 53^o \hat{i} + \sin 53^o \hat{j}) = 250(0.6 \hat{i} + 0.8 \hat{j}) = 150 \hat{i} + 200 \hat{j}\ m/s$.The absolute velocity of shell $2$ is $\vec{v}_2 = \vec{v}_{2J} + \vec{v}_J = (150 \hat{i} + 200 \hat{j}) + 10 \hat{i} = 160 \hat{i} + 200 \hat{j}\ m/s$.Since both shells are under gravity,their relative acceleration is $\vec{a}_{21} = \vec{a}_2 - \vec{a}_1 = (-g \hat{j}) - (-g \hat{j}) = 0$. Thus,the relative motion is uniform.The relative velocity is $\vec{v}_{21} = \vec{v}_2 - \vec{v}_1 = (160 \hat{i} + 200 \hat{j}) - (160 \hat{i} + 120 \hat{j}) = 80 \hat{j}\ m/s$.The initial relative position is $\vec{r}_{21} = \vec{r}_2 - \vec{r}_1 = (0, 0) - (0, 80) = -80 \hat{j}\ m$.The relative position at time $t$ is $\vec{r}(t) = \vec{r}_{21} + \vec{v}_{21} t = -80 \hat{j} + 80t \hat{j} = 80(t-1) \hat{j}$.The shells are closest when the magnitude of the relative position vector is minimum,which occurs at $t = 1\ s$,where the relative distance is $0$.

Similar Questions

$A$ ship $X$ moving due north with speed $v$ observes that another ship $Y$ is moving due west with the same speed $v$. The actual velocity of $Y$ is $........$.

$A$ boat crossing a river moves with a velocity $v$ relative to still water. The river is flowing with a velocity $v/2$ with respect to the bank. The angle with respect to the flow direction with which the boat should move to minimize the drift is (in $^{\circ}$)

It takes $1$ minute for a passenger standing on an escalator to reach the top. If the escalator does not move,it takes him $3$ minutes to walk up. How many seconds will it take for the passenger to arrive at the top if he walks up the moving escalator?

$A$ person walks up a stalled escalator in $90 \, s$. When just standing on the same moving escalator,he is carried in $60 \, s$. The time it would take him to walk up the moving escalator will be $....... \, s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module