If you throw a ball into the air at some angle with respect to the horizontal, which of the following statements about the ball is true?
The acceleration is zero at the top of the motion
The horizontal component of the velocity is zero at the top of the motion
The velocity is constant during the motion
The vertical component of the velocity is constant during the motion
The horizontal component of the acceleration is zero at the top of the motion
The vertical component of the acceleration changes sign at the top of the motion
The velocity is zero at the top of the motion
When a ball is thrown into the air at some angle with respect to the horizontal, the following statements about the ball are true:
1. The acceleration is zero at the top of the motion: This statement is true. At the very top of the ball's trajectory, the vertical (upward) component of the acceleration due to gravity cancels out the downward gravitational acceleration, resulting in zero net acceleration.
2. The horizontal component of the velocity is zero at the top of the motion: This statement is false. The horizontal component of the velocity remains constant throughout the motion, as there is no horizontal force acting on the ball to change its velocity.
3. The velocity is constant during the motion: This statement is false. The velocity of the ball changes throughout its motion due to the acceleration of gravity pulling it downwards. As the ball goes up, its velocity decreases until it reaches the top, and then it increases as it falls downwards.
4. The vertical component of the velocity is constant during the motion: This statement is false. The vertical component of the velocity changes during the ball's motion due to the acceleration of gravity. As the ball goes up, the velocity decreases, and as it falls downwards, the velocity increases.
5. The horizontal component of the acceleration is zero at the top of the motion: This statement is true. Since there is no horizontal force acting on the ball, the horizontal component of the acceleration is always zero throughout the motion.
6. The vertical component of the acceleration changes sign at the top of the motion: This statement is true. As the ball goes up, the vertical component of the acceleration is negative (opposite to the direction of motion), and when it reaches the top, it changes sign and becomes positive (in the same direction as the motion).
7. The velocity is zero at the top of the motion: This statement is false. The velocity of the ball is not zero at the top of the motion. It is only zero for a brief moment at the highest point of the trajectory, after which it starts to decrease as the ball starts to fall back down.
To determine which of the given statements about the ball is true when you throw it into the air at some angle with respect to the horizontal, we need to analyze the motion of the ball.
When the ball is thrown into the air, it follows a projectile motion. This means that its motion can be broken down into two independent components: horizontal and vertical.
1. The acceleration is zero at the top of the motion: False. The ball experiences a constant acceleration due to gravity throughout its flight, and this acceleration acts vertically downwards. It is not zero at the top of the motion.
2. The horizontal component of the velocity is zero at the top of the motion: False. The horizontal component of velocity remains constant throughout the motion, assuming there is no air resistance. Therefore, it is not zero at the top of the motion.
3. The velocity is constant during the motion: False. The velocity of the ball changes continuously during its flight. As it moves upward, its velocity decreases due to the influence of gravity, until it reaches zero at the top of its trajectory. Then, as it falls back down, its velocity increases in magnitude until it reaches its initial velocity when it was thrown.
4. The vertical component of the velocity is constant during the motion: False. Similar to the previous point, the vertical component of velocity changes throughout the motion. It decreases as the ball moves upward until it reaches zero at the top of its trajectory, and then increases in magnitude as it falls back down.
5. The horizontal component of the acceleration is zero at the top of the motion: True. Since the horizontal component of the ball's velocity remains constant, there is no change in the horizontal acceleration. It remains zero throughout the motion.
6. The vertical component of the acceleration changes sign at the top of the motion: True. The vertical component of acceleration is always in the downward direction, due to the influence of gravity. As the ball moves upward, the acceleration decreases in magnitude until it reaches zero at the top of its trajectory. As it falls back down, the acceleration increases in magnitude (but still in the downward direction).
7. The velocity is zero at the top of the motion: True. At the top of the ball's trajectory, its vertical component of velocity becomes zero. This is the point where the ball changes direction from moving upward to moving downward. The horizontal component of velocity, however, does not become zero.
Therefore, the correct statements are:
- The horizontal component of the acceleration is zero at the top of the motion.
- The vertical component of the acceleration changes sign at the top of the motion.
- The velocity is zero at the top of the motion.