A tennis ball is hit into the air and moves along an arc. Neglecting air resistance, where along the arc is the speed of the ball a)a minimum and b) a maximum?
I'm thinking it's at a max at the begging and end, and a min at the top, but that's just a guess.
Your guess is correct. Where potential energy is a maximum (at maximum height) the kinetic energy (and speed) must be a minimum. Where potential energy is a minium (a ground level) the kinetic energy (and speed) must be a maximum. If the ball went over a cliff, the speed would continue to increase until it hit the ground below.
Well, well, well! A tennis ball on an arc, huh? Let me give you the low-down on its speed. If we disregard air resistance, we can solve this puzzle.
When the ball is at the very beginning of its arc, also known as the launch, its speed is at a maximum. It's like when you're in a hurry to finish all your work during naptime at the circus - maximum speed, my friend!
Now, as the ball reaches the top of the arc, the speed comes screeching to a minimum. It's like when you're trying to juggle with slippery bananas - things slow down, don't they?
Finally, when the ball reaches the end of its arc, the speed is once again at a maximum. It's like when the circus train is about to leave town - gotta go fast, right?
So, to summarize, the speed of the ball is a maximum at the launch and the end of the arc, and a minimum at the top. Keep swinging those tennis rackets, my friend!
You are correct! The speed of the tennis ball is at a maximum at the beginning and the end of its trajectory, and it is at a minimum at the top of its trajectory. Let me explain why.
When the tennis ball is hit, it moves in a curved path called a projectile motion. The speed of the ball depends on its vertical and horizontal components of motion.
At the beginning of its trajectory, the ball is moving purely horizontally, so the vertical component of motion is zero. The entire initial velocity is in the horizontal direction, making the speed at its maximum.
As the ball rises, the vertical component of motion increases while the horizontal component remains constant. At the top of the arc, called the peak or maximum height, the vertical component of motion is at a maximum, but the horizontal component is still constant. This means that the overall speed at this point is at a minimum.
As the ball falls back down, the vertical component of motion decreases, while the horizontal component remains constant. At the end of its trajectory, the ball is again moving purely horizontally, so the vertical component of motion is zero. The entire final velocity is in the horizontal direction, making the speed once again at its maximum.
In summary, the tennis ball's speed is at a maximum at the beginning and end of its trajectory when it is moving purely horizontally, and it is at a minimum at the top of its trajectory when it reaches its maximum height.
You are correct in thinking that the speed of the tennis ball is at a maximum at the beginning and end of the arc, and at a minimum at the top. Let's understand why this is the case.
When a tennis ball is hit into the air, it follows a projectile motion trajectory, forming an arc. This motion can be broken down into two components: horizontal motion (along the x-axis) and vertical motion (along the y-axis).
Since air resistance is neglected, the only force acting on the ball is gravity, which constantly accelerates it downward. This acceleration affects the vertical motion of the ball, but does not affect the horizontal motion (assuming the ball is not influenced by any external forces like wind).
Let's examine the key points along the arc where the speed is a maximum or a minimum:
a) At the beginning and end of the arc (the highest points of the arc), the ball momentarily comes to a stop before changing direction. At these points, the vertical velocity becomes zero (reaches its maximum height) while the horizontal velocity remains constant. The speed of the ball is purely determined by its horizontal velocity, so it is at a maximum.
b) At the top of the arc, where the ball reaches its maximum height, the vertical velocity is momentarily zero and the ball starts moving downwards. Here, both the vertical and horizontal components of velocity contribute to the ball's total speed. Since the horizontal velocity remains constant while the vertical velocity decreases, the speed of the ball is at a minimum.
To summarize:
- At the beginning and end of the arc, the speed of the ball is at a maximum.
- At the top of the arc, the speed of the ball is at a minimum.
It's important to note that neglecting air resistance is an idealized scenario. In reality, air resistance would affect the speed of the ball throughout its entire trajectory.