Bennett Mechanical Velocity and Gravity Questions and Answers 1 — Questions and Answers
Question 1: Ignoring air resistance, if a 1kg stone and a 10kg cannonball are dropped from the same height at the same time, which will hit the ground first?
- The 10kg cannonball
- The 1kg stone
- They will hit the ground at the same time (Correct answer)
- It depends on the shape of the objects
Correct answer: They will hit the ground at the same time
In a vacuum or when air resistance is ignored, all objects fall at the same rate of acceleration due to gravity (approximately 9.8 m/s² on Earth), regardless of their mass. While gravity exerts a greater force on the more massive object (the cannonball), that object also has greater inertia (resistance to acceleration). These two effects cancel each other out, resulting in the same acceleration for both objects.
Question 2: A skydiver jumps from a plane. After a few seconds, she stops accelerating and falls at a constant speed. What is this constant speed called?
- Terminal velocity (Correct answer)
- Gravitational constant
- Escape velocity
- Maximum acceleration
Correct answer: Terminal velocity
Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium (like air) through which it is falling equals the force of gravity. At this point, the net force on the object is zero, and it stops accelerating, continuing to fall at a constant velocity.
Question 3: A ball is thrown horizontally off a cliff. At the exact same moment, an identical ball is dropped straight down from the same height. Ignoring air resistance, which of the following is true?
- The thrown ball hits the ground first.
- The dropped ball hits the ground first.
- They both hit the ground at the same time. (Correct answer)
- The thrown ball has a greater vertical velocity upon impact.
Correct answer: They both hit the ground at the same time.
The horizontal motion of an object is independent of its vertical motion. Both balls start with zero vertical velocity and are subject to the same downward acceleration due to gravity. Therefore, they will travel the same vertical distance in the same amount of time and hit the ground simultaneously. The thrown ball will have a greater overall speed upon impact because it has both horizontal and vertical velocity components, but its time in the air is determined solely by its vertical motion.
Question 4: A roller coaster car is at the top of a hill, momentarily motionless before it begins to descend. At this specific point, which statement best describes its energy?
- It has maximum kinetic energy and minimum potential energy.
- It has equal amounts of kinetic and potential energy.
- It has zero kinetic and zero potential energy.
- It has maximum potential energy and minimum kinetic energy. (Correct answer)
Correct answer: It has maximum potential energy and minimum kinetic energy.
Potential energy is stored energy due to an object's position or height, while kinetic energy is the energy of motion. At the highest point of its path, the roller coaster has the greatest height, so its gravitational potential energy is at a maximum. Since it is momentarily motionless, its velocity is zero, and therefore its kinetic energy is at a minimum (zero). As it rolls down, the potential energy is converted into kinetic energy.
Question 5: If you double the velocity of a moving object, what happens to its kinetic energy?
- It is halved.
- It doubles.
- It quadruples. (Correct answer)
- It does not change.
Correct answer: It quadruples.
The formula for kinetic energy (KE) is KE = 1/2 * mass * velocity². Because the velocity term is squared, doubling the velocity results in a fourfold increase in kinetic energy (2² = 4). For example, if the initial KE is 10 joules, doubling the velocity would make the new KE equal to 40 joules.
Question 6: An object is thrown straight up into the air. At the very peak of its trajectory, which of the following is true?
- Its velocity is at its maximum.
- Its acceleration is zero.
- Its velocity is zero, but its acceleration is not zero. (Correct answer)
- Its acceleration and velocity are both zero.
Correct answer: Its velocity is zero, but its acceleration is not zero.
At the peak of its trajectory, the object momentarily stops moving upwards before it begins to fall back down, so its instantaneous velocity is zero. However, the force of gravity is constantly acting on it, causing a constant downward acceleration (approximately 9.8 m/s²). Therefore, even when its velocity is zero at the top, its acceleration is not.
