Impulse (J) = mass (m) × change in velocity (Δv) = 0.5 kg × (10 m/s - 0 m/s) = 5 Ns.

In a perfectly elastic collision, momentum is conserved. Initial momentum = 1 kg × 5 m/s = 5 kg·m/s.

Using conservation of energy: Potential Energy = Kinetic Energy. mgh = 0.5mv². v = sqrt(2gh) = sqrt(2 × 9.8 m/s² × 20 m) = 20 m/s.

Using F = ma, we find acceleration: a = F/m = 30 N / 15 kg = 2 m/s².

Net force = mass * acceleration = 2 kg * 3 m/s² = 6 N. The applied force is 10 N, so frictional force = applied force - net force = 10 N - 6 N = 4 N.

Total momentum = momentum of 2 kg object + momentum of 3 kg object = (2 kg × 10 m/s) + (3 kg × 0 m/s) = 20 kg·m/s.

Momentum (p) = mass (m) × velocity (v) => velocity (v) = p/m = 12 kg·m/s / 3 kg = 4 m/s.

Momentum = mass × velocity = 3 kg × 10 m/s = 30 kg·m/s.

Impulse (J) = change in momentum = mass (m) × change in velocity (Δv) = 4 kg × (0 - 6 m/s) = -24 Ns.

Momentum (p) = mass (m) × velocity (v) = 5 kg × 3 m/s = 15 kg·m/s.

Using the formula t = √(2h/g), where h = 45 m and g = 9.8 m/s², we get t = √(2 * 45 / 9.8) ≈ 3.06 s.

Using the formula t = √(2h/g), where h = 45 m and g = 9.8 m/s², we get t = √(2 * 45 / 9.8) ≈ 3.03 s.

The resultant speed is found using the Pythagorean theorem: √(8^2 + 3^2) = √(64 + 9) = √73 ≈ 8.6 km/h.

The speed of the boat relative to the riverbank is the speed of the boat minus the speed of the river: 10 km/h - 5 km/h = 5 km/h.

Charge (Q) is given by Q = CV. Here, Q = 3 µF * 15 V = 45 µC.

If the voltage is doubled, the charge on the capacitor also doubles, since Q = C * V.

Energy stored, U = 0.5 * C * V² = 0.5 * 10 x 10^-6 F * (5 V)² = 0.125 mJ.

The charge stored in a capacitor is given by Q = C * V = 10μF * 5V = 50μC.

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

The speed of the second car relative to the first car is 80 km/h - 60 km/h = 20 km/h.

Using the Doppler effect formula, f' = f(v + vo) / (v - vs), where v = 340 m/s, vo = 0, vs = 30 m/s, f' = 500(340)/(340 - 30) = 500(340/310) ≈ 548 Hz.

Impulse (J) = change in momentum = mass (m) × change in velocity (Δv) = 1000 kg × (0 - 20 m/s) = -20000 Ns.

The child's speed relative to the ground is 15 m/s + 5 m/s = 20 m/s.

Tension provides the centripetal force: T = mv²/r = 0.5 kg * (4 m/s)² / 2 m = 8 N.

Using Ohm's Law, I = V/R. Here, I = 12V / 3Ω = 4 A.

Acceleration = (final velocity - initial velocity) / time = (15 m/s - 0) / 10 s = 1.5 m/s².

The cyclist's speed relative to the ground is 15 km/h + 5 km/h = 20 km/h.

Average speed = total distance / total time = 100 m / 5 s = 20 m/s.

The cyclist's speed relative to the road is simply the speed of the cyclist: 15 km/h.

Using v = rω, we have ω = v/r = 2 m/s / 0.5 m = 4 rad/s.