Maria throws a ball straight up with an initial velocity of 10 m/s.
A. What is its velocity at the highest point?
B. What is its velocity when it returned to the elevation from where it was thrown?
C. What is its acceleration at the highest point?
D. What is its acceleration just before it hits the ground?
E. After 1 second, what is the acceleration of the ball?
A. Oh, you know, at the highest point, the ball is like, "Hey, I've reached my peak!" So its velocity is, drumroll please, zero! It's taking a little break before it comes back down.
B. When the ball is back to where it started, it's like, "Whoa, what a journey! I'm finally home!" So its velocity is also 10 m/s, but in the opposite direction. It's a bittersweet reunion.
C. At the highest point, the ball has reached its pinnacle, but gravity is like, "I'm still gonna pull you down!" So the acceleration at the highest point is -9.8 m/s². Negative because gravity is pulling downwards, and 9.8 m/s² because, well, that's just how gravity rolls here on Earth.
D. Just before the ball hits the ground, gravity is like, "Prepare for the grand finale, my friend!" So the acceleration right before it hits the ground is still -9.8 m/s². It's like gravity's closing act.
E. After 1 second, the acceleration of the ball is still -9.8 m/s². Gravity doesn't take any breaks, my friend! It's always there, pulling things down, making sure we stay grounded. Just like that one friend who always brings us back to reality.
To answer these questions, we will assume that air resistance is negligible.
A. At the highest point, the velocity of the ball is 0 m/s. This is because at the highest point of its trajectory, the ball momentarily stops moving upward and begins to fall downward.
B. When the ball returns to the elevation from where it was thrown, its velocity will be -10 m/s. The negative sign indicates that the ball is now moving in the opposite direction (downwards) compared to when it was thrown.
C. At the highest point, the acceleration of the ball is equal to the acceleration due to gravity, which is approximately -9.8 m/s^2. The negative sign indicates that acceleration is directed downward.
D. Just before it hits the ground, the magnitude of the ball's acceleration remains the same, approximately -9.8 m/s^2. However, the direction of acceleration changes to be positive, as it opposes the downward velocity and causes the ball to slow down before coming to a stop.
E. After 1 second, the acceleration of the ball remains the same as before, approximately -9.8 m/s^2. The time duration does not affect the acceleration value.
To answer these questions, we need to understand the basic principles of motion and the equations that govern it.
1. Velocity at the highest point:
When the ball reaches the highest point of its trajectory, its vertical velocity becomes zero. This is because the ball momentarily stops moving upwards before it starts to descend. Therefore, the velocity at the highest point is zero.
2. Velocity when it returns to the elevation from where it was thrown:
When the ball returns to its original elevation, it will have the same magnitude of velocity as when it was thrown, but in the opposite direction. So the velocity will be -10 m/s (negative since it's directed downwards).
3. Acceleration at the highest point:
At the highest point, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s². This acceleration is directed towards the center of the Earth.
4. Acceleration just before it hits the ground:
Just before the ball hits the ground, the acceleration remains the same as throughout the motion, which is 9.8 m/s² directed towards the center of the Earth.
5. Acceleration after 1 second:
To find the acceleration after 1 second, we need to know if the ball is still in its upward motion or if it has already started falling. Assuming the ball is in the upward motion for 1 second, we can calculate the acceleration using the equation of motion:
v = u + at
Since the initial velocity (u) is 10 m/s and the time (t) is 1 second, we can rearrange the equation to solve for acceleration (a):
a = (v - u) / t
a = (0 - 10) / 1
Therefore, the acceleration after 1 second is -10 m/s² (negative since it's directed downwards).
It's important to note that these answers are based on the idealized motion of a ball thrown straight up in the absence of air resistance. In reality, factors like air resistance can affect the motion of the ball, leading to slight variations in the answers.