Maximum Height (h) = v^2 / (2g) = (20 m/s)^2 / (2 * 10 m/s²) = 20 m

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 1 kg * (4 m/s)^2 = 8 J.

Using conservation of energy, PE at top = KE at bottom. mgh = 1/2 mv^2. 10 kg * 9.8 m/s^2 * 5 m = 1/2 * 10 kg * v^2. Solving gives v = 10 m/s.

Using conservation of energy, PE at top = KE at bottom: mgh = 1/2 mv²; v = sqrt(2gh) = sqrt(2 * 10 m/s² * 5 m) = 10 m/s

Potential Energy (PE) = m * g * h = 10 kg * 10 m/s² * 20 m = 2000 J

Using the formula v = √(2gh) = √(2 * 10 m/s² * 20 m) = √400 = 20 m/s.

Potential Energy (PE) = m * g * h = 10 kg * 9.8 m/s^2 * 5 m = 490 J.

Total Mechanical Energy = Kinetic Energy + Potential Energy = (1/2 * 10 kg * (4 m/s)²) + (10 kg * 9.8 m/s² * 5 m) = 80 J + 490 J = 570 J

Using energy conservation, v = sqrt(2gh) = sqrt(2 * 9.8 m/s² * 10 m) = 14 m/s.

Using conservation of energy, Potential Energy at height = Kinetic Energy just before hitting ground. mgh = 1/2 mv^2. Solving gives v = sqrt(2gh) = sqrt(2 * 10 m/s² * 10 m) = 14.14 m/s.

Using energy conservation, Potential Energy = Kinetic Energy at the ground: mgh = 0.5 mv^2; v = sqrt(2gh) = sqrt(2 * 10 m/s² * 20 m) = 20 m/s

Using conservation of energy, Potential Energy at top = Kinetic Energy at bottom: mgh = 1/2 mv^2; v = sqrt(2gh) = sqrt(2 * 9.8 m/s² * 3 m) = 7.75 m/s (approx. 6 m/s)

Using the formula v = √(2gh) = √(2 * 10 m/s² * 20 m) = √400 = 20 m/s

Work Done (W) = m * g * h = 2 kg * 9.8 m/s^2 * 3 m = 58.8 J (approx. 60 J)

Work Done = mgh = 2 kg * 9.8 m/s² * 3 m = 58.8 J

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 2 kg * (4 m/s)^2 = 16 J.

Momentum (p) = m * v = 2 kg * 4 m/s = 8 kg m/s

Using conservation of energy, PE = KE: mgh = 1/2 mv²; v = sqrt(2gh) = sqrt(2 * 10 m/s² * 12 m) = 15.49 m/s

Potential Energy (PE) = m * g * h = 3 kg * 9.8 m/s^2 * 4 m = 117.6 J (approximately 120 J)

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 3 kg * (2 m/s)^2 = 6 J

Momentum (p) = mv = 3 kg * 6 m/s = 18 kg m/s

Using the formula v^2 = u^2 - 2gh, we find h = u^2 / (2g) = (15 m/s)^2 / (2 * 9.8 m/s²) = 11.5 m.

Work Done = Change in Kinetic Energy = 1/2 * m * (v^2 - u^2) = 1/2 * 1000 kg * (20 m/s)^2 = 200,000 J

Kinetic Energy is proportional to the square of the speed. If speed is doubled, KE increases by a factor of 2^2 = 4.

Kinetic Energy is proportional to the square of the speed. If speed is doubled, KE increases by a factor of 2^2 = 4.

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 75 kg * (15 m/s)^2 = 8437.5 J.

Potential Energy (PE) = 1/2 * k * x^2 = 1/2 * 200 N/m * (0.1 m)^2 = 1 J

Potential Energy in Spring (PE) = 1/2 kx^2 = 1/2 * 500 N/m * (0.2 m)^2 = 10 J

Potential Energy (PE) = m * g * h = 5 kg * 9.8 m/s^2 * 20 m = 980 J (approximately 400 J for 1 kg)

Work Done = m * g * h = 10 kg * 9.8 m/s² * 4 m = 392 J (approx. 400 J).