Potential energy PE = mgh = 15 kg * 9.81 m/s² * 20 m = 2943 J.

Impulse (J) = change in momentum = mass (m) × velocity (v) = 2 kg × 4 m/s = 8 Ns.

Potential Energy = mgh = 2 kg × 9.8 m/s² × 3 m = 58.8 J.

Work done W = mgh = 2 kg * 9.81 m/s² * 5 m = 98.1 J.

Momentum is calculated using the formula p = mv. Thus, p = 2 kg * 3 m/s = 6 kg·m/s.

In an elastic collision, the velocities are exchanged. The first object comes to rest, so final velocity = 0 m/s.

Using Newton's second law, F = ma, we can find acceleration: a = F/m = 15 N / 5 kg = 3 m/s².

Average acceleration (a) = (final velocity - initial velocity) / time = (20 m/s - 0 m/s) / 5 s = 4 m/s².

Work done = Change in Kinetic Energy = 0.5 × 1000 kg × (20 m/s)² = 200000 J. Power = Work / Time = 200000 J / 5 s = 40000 W.

Work done = Change in Kinetic Energy = 0.5 × 1000 kg × (20 m/s)² = 200000 J. Power = Work / Time = 200000 J / 10 s = 20000 W.

Acceleration is calculated using the formula a = (v - u)/t. Here, a = (20 m/s - 0)/5 s = 4 m/s².

The speed of the cyclist relative to the car is the sum of their speeds since they are moving in opposite directions: 80 km/h + 20 km/h = 100 km/h.

Distance = speed × time = 60 km/h × 2 h = 120 km.

Deceleration a = (final velocity - initial velocity) / time = (0 - 20 m/s) / 5 s = -4 m/s².

Average speed is calculated as speed = distance/time, so speed = 100 m / 5 s = 20 m/s.

The induced emf is proportional to both the speed of the conductor and the length of the conductor when moving perpendicular to the magnetic field.

Using F = ma, we find acceleration: a = F/m = 15 N / 3 kg = 5 m/s².

Work = Force × Distance = 15 N × 4 m = 60 J.

A particle moving in a circular path with constant speed experiences centripetal acceleration directed towards the center of the circle.

Impulse is defined as the change in momentum of an object, which is calculated as the difference between the final and initial momentum, J = p2 - p1.

The person's speed relative to the ground is 60 km/h + 4 km/h = 64 km/h.

The plane's speed relative to the ground is the speed of the plane minus the speed of the wind: 200 km/h - 50 km/h = 150 km/h.

If no external torques act on the body, the angular velocity can remain constant during rotation.

The angular speed (ω) can be calculated using the formula ω = v/r. Here, ω = 2 m/s / 0.5 m = 4 rad/s.

The angular speed (ω) of a rolling object is related to its translational speed (v) by the equation ω = v/r.

Using KE = (1/2)Iω², we have 50 J = (1/2)(5 kg·m²)ω², solving gives ω = 10 rad/s.

Torque is calculated as τ = I * α, where I is the moment of inertia and α is the angular acceleration. Here, τ = 2 kg·m² * 3 rad/s² = 6 N·m.

Rotational kinetic energy is given by KE = 0.5 Iω² = 0.5 * 4 kg·m² * (3 rad/s)² = 18 J.

Using L = Iω, we find ω = L/I = 20 kg·m²/s / 4 kg·m² = 5 rad/s.

The solid sphere has a lower moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.