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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?
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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?
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