Physics Fundamentals: Motion, Energy, and Momentum

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A rock is thrown upwards from the ground with an initial velocity of 20 m/s. If the acceleration due to gravity is 9.8 m/s², how long will it take for the rock to reach its maximum height? Assume the rock starts from rest.

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.

A car travels horizontally at a constant velocity of 30 m/s. If the car travels for 10 seconds, how far will it have traveled?

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.

A baseball is thrown with an initial velocity of 25 m/s at an angle of 30° to the horizontal. If the acceleration due to gravity is 9.8 m/s², find the range of the baseball. Assume the ball starts from the ground.

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.

A 2 kg block is moving at a velocity of 5 m/s. If it collides with a 3 kg block at rest, what is the resulting velocity of the system if the collision is elastic?

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. Signup and view all the answers

A 10 kg block is lifted 2 m vertically upwards. If the gravitational acceleration is 9.8 m/s², what is the increase in potential energy of the block?

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. Signup and view all the answers

A body is projected upwards from the ground with an initial velocity of 15 m/s. If the acceleration due to gravity is 9.8 m/s², what is the velocity of the body when it reaches a height of 10 m?

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. Signup and view all the answers

A projectile is fired at an angle of 45° to the horizontal with an initial velocity of 20 m/s. If the acceleration due to gravity is 9.8 m/s², find the horizontal component of its velocity when it reaches the ground.

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. Signup and view all the answers

A force of 10 N is applied to a 5 kg block for 2 seconds. If the block is initially at rest, what is its resulting velocity?

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. Signup and view all the answers

A 2 kg block is moving at a velocity of 3 m/s when it collides with a stationary 1 kg block. If the collision is inelastic, what is the resulting velocity of the combined system?

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. Signup and view all the answers

A motor lifts a 50 kg box to a height of 5 m in 10 seconds. If the efficiency of the motor is 80%, what is the power output of the motor?

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. Signup and view all the answers

Physics Fundamentals: Motion, Energy, and Momentum

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Questions and Answers

A rock is thrown upwards from the ground with an initial velocity of 20 m/s. If the acceleration due to gravity is 9.8 m/s², how long will it take for the rock to reach its maximum height? Assume the rock starts from rest.

A car travels horizontally at a constant velocity of 30 m/s. If the car travels for 10 seconds, how far will it have traveled?

A baseball is thrown with an initial velocity of 25 m/s at an angle of 30° to the horizontal. If the acceleration due to gravity is 9.8 m/s², find the range of the baseball. Assume the ball starts from the ground.

A 2 kg block is moving at a velocity of 5 m/s. If it collides with a 3 kg block at rest, what is the resulting velocity of the system if the collision is elastic?

A 10 kg block is lifted 2 m vertically upwards. If the gravitational acceleration is 9.8 m/s², what is the increase in potential energy of the block?

A body is projected upwards from the ground with an initial velocity of 15 m/s. If the acceleration due to gravity is 9.8 m/s², what is the velocity of the body when it reaches a height of 10 m?

A projectile is fired at an angle of 45° to the horizontal with an initial velocity of 20 m/s. If the acceleration due to gravity is 9.8 m/s², find the horizontal component of its velocity when it reaches the ground.

A force of 10 N is applied to a 5 kg block for 2 seconds. If the block is initially at rest, what is its resulting velocity?

A 2 kg block is moving at a velocity of 3 m/s when it collides with a stationary 1 kg block. If the collision is inelastic, what is the resulting velocity of the combined system?

A motor lifts a 50 kg box to a height of 5 m in 10 seconds. If the efficiency of the motor is 80%, what is the power output of the motor?

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