Explanation

When two bodies A and B are moving parallel along a straight line, the relative velocity of A with respect to B is given by:

V_AB = V_A - V_B

Explanation

The scalar product (dot product) of two vectors A and B is given by:

A · B = |A| |B| cos(θ)

Maximum value occurs when cos(θ) = 1 (θ = 0°)

Let's find the angle where the scalar product is half of its maximum value:

|A| |B| cos(θ) = (1/2) |A| |B|

cos(θ) = 1/2

θ = 60°

Explanation

Given:

Initial velocity (u) = 0 m/s (starts from rest)

Final velocity (v) = 100 m/s

Time (t) = 10 s

Acceleration (a) = (v - u) / t

a = (100 m/s - 0 m/s) / 10 s

a = 100 m/s / 10 s

a = 10 m/s²

Explanation

In interference, silence zones (or nodes) occur where the path difference between two sound waves is equal to an odd multiple of λ/2.

Path difference = (2n + 1)λ/2, where n = 0, 1, 2, ...

For the simplest case, n = 0:

Path difference = λ/2

Explanation

Given:

Time (t) = 10 seconds

Initial velocity (u) = 0 (since it's free fall from rest)

Acceleration due to gravity (g) = 10 m/s² (approx.)

Distance covered (s) = ut + (1/2)gt²

Since u = 0, s = (1/2)gt²

s = (1/2) × 10 × 10²

s = 5 × 100

s = 500 m

Explanation

When a cyclist takes a turn, they bend inward so that the resultant of their weight and the centripetal force passes through the center of gravity.

Bending provides the required centripetal force for circular motion.

Without bending, the cyclist would topple outward.

Explanation

Given:

Change in momentum (Δp) = 5 kg m/s

Time interval (Δt) = 2 seconds

Force (F) is given by the formula: F = Δp / Δt

F = 5 kg m/s / 2 s

F = 2.5 N

Explanation

• Light travels from denser to rarer medium.
• Angle of incidence > Critical angle.

Explanation

In SHM, the total distance covered by a body in one complete oscillation is equal to 4 times the amplitude (A).

Let's break it down:

• The body moves from its equilibrium position to the extreme position (distance = A)
• Then, it moves to the other extreme position (distance = 2A)
• Finally, it returns to the equilibrium position (distance = A) and then to the initial extreme position is not needed as it completes the cycle at the equilibrium position coming from the second extreme, so from the second extreme to equilibrium is A, and from equilibrium to the first extreme is A, totaling 4A for the full cycle.

Explanation

Hooke’s law states that stress is directly proportional to strain within the elastic limit.

It defines the proportionality range between stress and strain.

Beyond this limit, permanent deformation occurs.