Test: Relative Velocity in Two Dimensions - ACT MCQ

The body’s displacement is given by s = (1/2)at². Therefore, after putting in the values, we get, s = (1/2)(11î + 2ĵ)*10² = 550î + 100ĵ. The body initially starts from î + ĵ. Hence, the final position is = initial position + displacement = 551î + 101ĵ.

The body’s displacement is given by s = vt. The body starts from the origin hence, the total displacement is the final position of the body. Therefore, after putting in the values, we get, s = (4î + 3ĵ)*10 = 40î + 30ĵ.

The velocity of the man is 25î – 75ĵ and that of the woman is -75î + 25ĵ. Relative velocity = velocity of man – velocity of woman = 100î – 100ĵ.

The formula for calculating relative velocity of a body with respect to another body is- relative velocity = Velocity vector of A – Velocity vector of B. Hence, here, the relative velocity = velocity of B – velocity of A = 6î – 6ĵ.

The body’s displacement is given by s = (1/2)at². The body starts from the origin hence, the total displacement is the final position of the body. Therefore, after putting in the values, we get, s = (1/2)(4î + 3ĵ)*5² = 50î + 37.5ĵ.

The velocity of the man is 15î+3ĵ and that of the woman is 17î + 7ĵ. Relative velocity = velocity of dog – velocity of pig = -2î – 4ĵ.

The formula for calculating relative velocity of a body with respect to another body is- relative velocity = Velocity vector of A – Velocity vector of B. Hence, here, the relative velocity = velocity of B – velocity of A = -17î + 7ĵ.

Concept:

A) When two bodies move uniformly in opposite direction, the velocities gets added up.

B) When two bodies move uniformly in same direction, the velocities gets subtracted.

Calculation:

Given:

Let one bodies be A and B, and theor speed be V and U respectively.

As per the problem;

V_A + V_B = 6  ------(i)

V_A - V_B = 4  ------(ii)

Adding eq (i) and eq (ii)

2VA = 10

∴ VA = 5 m/s

Similarly

VA + VB = 6

5 + VB = 6

∴ VB  = 1 m/s

In the situation of a stationary escalator and moving girl velocity,

In the situation of stationary girl and moving escalator velocity,

If both escalator and girl keep moving then distance,
L = (V + V₁) t₃   ----(3)
Where t₃ is time to cover that distance when both girl and the escalator keep moving.
Using equations (1), (2), and (3) we get:

Then, time is taken 

Formula Used:
Velocity = s/t
Here, S is displacement and t is time
For instantaneous velocity, it expressed as dS/dt
Application:
We have,
S = 3t² - 5t + 7
Hence,
Instantaneous velocity = dS/dt = (6t - 5)
initial velocity will be found at t = o
Hence,
V|_initial = (6 × 0 - 5) = - 5