# Physics Problems: Motion, Energy, and Work

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## 5 Questions

### A rock is dropped from a height of 20 m. If air resistance is negligible, what is the speed of the rock just before it hits the ground? (Assume g = 9.8 m/s^2)

v = √(2gh) = √(2 * 9.8 * 20) = 14 m/s

### A baseball is thrown horizontally from a cliff with an initial velocity of 20 m/s. If the cliff is 50 m high, how far does the baseball travel horizontally before hitting the ground? (Assume g = 9.8 m/s^2)

Use the equation for horizontal motion: x = v₀t. First, find the time it takes to hit the ground: t = √(2h/g) = √(2*50/9.8) = 3.2 s. Then, x = 20 m/s * 3.2 s = 64 m

### A 2 kg block is attached to a horizontal, massless spring with a force constant of 100 N/m. If the block is displaced 0.2 m from equilibrium and released, what is its speed when it passes through the equilibrium position?

Use the equation for potential energy: PE = (1/2)kx². The block starts with 0.5 J of potential energy, which is converted to kinetic energy as it passes through the equilibrium position. So, 0.5 J = (1/2)mv², and v = √(2*0.5/2) = 1 m/s

### A 5 kg block is moving at 2 m/s when it collides with a stationary 3 kg block. If the blocks stick together after the collision, what is their final velocity?

Use the principle of conservation of momentum: p₁ = p₂. The initial momentum is 5 kg * 2 m/s = 10 kg m/s. The final momentum is (5 kg + 3 kg) * v. Equating the two, 10 kg m/s = 8 kg * v, and v = 1.25 m/s

### A 10 V battery is connected to a 2 Ω resistor and a 0.1 H inductor in series. If the switch is closed at t = 0, what is the current through the resistor at t = 0.01 s?

Use the equation for electrical energy: I = ε / R, and the concept of inductance to solve this problem.

Test your understanding of fundamental physics concepts with this collection of problems and solutions. Covers vertical motion, horizontal motion, projectile motion, conservation of momentum, potential energy, work, and electrical energy. Improve your problem-solving skills and prepare for exams.

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