What are the speeds of two objects if,when th | vedclass

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

Question

(D) Let the speeds of the two objects be $v_A$ and $v_B$ (where $v_A > v_B$).When they move towards each other,their relative speed is the sum of thei

Vedclass · Accepted Answer

$2.2\,m/s$ and $1.8\,m/s$

Vedclass · Answer

(D) Let the speeds of the two objects be $v_A$ and $v_B$ (where $v_A > v_B$).When they move towards each other,their relative speed is the sum of their individual speeds: $v_{rel} = v_A + v_B$.Given that they get $4\,m$ closer in $1\,s$,the relative speed is $v_A + v_B = \frac{4\,m}{1\,s} = 4\,m/s$ (Equation $1$).When they move in the same direction,their relative speed is the difference of their individual speeds: $v_{rel} = v_A - v_B$.Given that they get $4.0\,m$ closer in $10\,s$,the relative speed is $v_A - v_B = \frac{4.0\,m}{10\,s} = 0.4\,m/s$ (Equation $2$).Adding Equation $1$ and Equation $2$: $(v_A + v_B) + (v_A - v_B) = 4 + 0.4 \implies 2v_A = 4.4 \implies v_A = 2.2\,m/s$.Subtracting Equation $2$ from Equation $1$: $(v_A + v_B) - (v_A - v_B) = 4 - 0.4 \implies 2v_B = 3.6 \implies v_B = 1.8\,m/s$.Thus,the speeds are $2.2\,m/s$ and $1.8\,m/s$.

What are the speeds of two objects if,when they move uniformly towards each other,they get $4\,m$ closer in each second and when they move uniformly in the same direction with the original speeds,they get $4.0\,m$ closer each $10\,s$?

Similar Questions

$A$ stone falls from the top of a tower of height $100 \text{ m}$ and at the same time another stone is projected vertically upwards from the ground with a velocity $25 \text{ m/s}$. The two stones meet after (in $\text{ s}$)

Two particles are at rest on a straight track and they are separated from each other by $100 \ m$. They start their motion in the same direction,with the same acceleration $10 \ m/s^2$. Their relative displacement after $10 \ s$ will be

Two cars are travelling towards each other at a speed of $20 \,m \,s^{-1}$ each. When the cars are $300 \,m$ apart, both the drivers apply brakes and the cars retard at the rate of $2 \,m \,s^{-2}$. The distance between them when they come to rest is: (in $\,m$)

Two cars $A$ and $B$ are travelling in the same direction with velocities $V_A$ and $V_B$ $(V_A > V_B)$. When the car $A$ is at a distance $S$ behind the car $B$,the driver of the car $A$ applies the brakes producing a uniform retardation $a$. There will be no collision when:

Explain the concept of relative velocity and its two cases.

Vedclass Test Series

Exam Paper Generator

Online Exam Module