Physics Fundamentals: Motion, Energy, and Momentum

Using the equation of motion v = u + at, we can find the time it takes for the rock to reach its maximum height, where v = 0 m/s. Solving for t, we get t = u / a = 20 m/s / 9.8 m/s² = 2.04 s.

Using the equation of motion s = vt, we can find the distance traveled by the car. Substituting the values, we get s = vt = 30 m/s × 10 s = 300 m.

Using the equation for range R = (u² sin 2θ) / g, we can find the range of the baseball. Substituting the values, we get R = (25² sin 2(30°)) / 9.8 m/s² = 55.4 m.

<p>Using the principle of conservation of momentum, we can find the resulting velocity of the system. The total momentum before the collision is p₁ = 2 kg × 5 m/s = 10 kg m/s. After the collision, the total momentum is conserved, and the resulting velocity is v = p₁ / (m₁ + m₂) = 10 kg m/s / (2 kg + 3 kg) = 2 m/s.</p> Signup and view all the answers

<p>Using the equation for potential energy ΔU = mgh, we can find the increase in potential energy of the block. Substituting the values, we get ΔU = 10 kg × 9.8 m/s² × 2 m = 196 J.</p> Signup and view all the answers

<p>Using v² = u² + 2as, where v = final velocity, u = initial velocity, a = acceleration, s = displacement. v² = 15² + 2(-9.8)(10) = 0, hence v = 0 m/s.</p> Signup and view all the answers

<p>Resolve the initial velocity into horizontal and vertical components. The horizontal component is given by ucos(45°) = 20cos(45°) = 14.14 m/s. Since the horizontal component remains constant, the horizontal velocity when it reaches the ground is still 14.14 m/s.</p> Signup and view all the answers

<p>Using the impulse-momentum theorem, Δp = FΔt, where Δp = change in momentum, F = force, Δt = time. Δp = 10(2) = 20 kgm/s. Since the block is initially at rest, the resulting momentum is equal to the change in momentum. Hence, mv = 20, where m = 5 kg. Solving for v, we get v = 4 m/s.</p> Signup and view all the answers

<p>Momentum is conserved in a closed system. Initial momentum = 2(3) = 6 kgm/s. Let the final velocity be v. Then, 6 = (2 + 1)v, v = 6/3 = 2 m/s.</p> Signup and view all the answers

<p>Work done = mgh = 50(9.8)(5) = 2450 J. Power = work done / time = 2450/10 = 245 W. Since the efficiency is 80%, the power output of the motor = 245/0.8 = 306.25 W.</p> Signup and view all the answers