Velocity when ball hits ground

In summary, the velocity of a ball when it hits the ground is affected by the initial height, gravitational acceleration, air resistance, and elasticity. The velocity can be calculated using the equation v = √(2gh), and it changes due to the conversion of potential energy into kinetic energy. The velocity can be greater than the initial velocity, but it cannot exceed the speed of light. The relationship between the velocity and the time it takes to hit the ground is described by the equation v = gt, with the velocity increasing as the time and gravitational acceleration increase.
  • #1
thedram
1
0

Homework Statement



The speed of a ball is v_b= L/t + gt/2 at a height h_b above the ground. What is velocity when ball hits ground?

Homework Equations



v^2 = v_i^2 + 2gh_b

The Attempt at a Solution



Tried v_2 = v_i^2 + sqrt 2gh_b This doesn't work . Any ideas
 
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  • #2
What answer did you arrive at? Show your work so we can know how far you are getting and where you got stuck.
 
  • #3
?

Assuming that the equation for the speed of the ball v_b is correct, we can use the equation for velocity when an object hits the ground to solve for the velocity when the ball hits the ground. The equation is v = sqrt(2gh), where v is the velocity, g is the acceleration due to gravity, and h is the height at which the object is dropped. In this case, the height at which the ball is dropped is h_b, so we can substitute that into the equation:

v = sqrt(2g*h_b)

Since we are looking for the velocity when the ball hits the ground, we can set h_b equal to 0, since the ball will be at ground level. This gives us:

v = sqrt(2g*0)

v = 0

Therefore, the velocity when the ball hits the ground is 0. This makes sense, as the ball will have come to a stop when it hits the ground.
 

What is the velocity of a ball when it hits the ground?

The velocity of a ball when it hits the ground depends on several factors, such as the initial height from which it was dropped, the gravitational acceleration, and the air resistance. However, assuming no air resistance and a constant gravitational acceleration of 9.8 m/s², the velocity of a ball when it hits the ground can be calculated using the equation: v = √(2gh), where g is the gravitational acceleration and h is the initial height.

Does the velocity of a ball change when it hits the ground?

Yes, the velocity of a ball changes when it hits the ground. This is due to the conservation of energy principle, which states that energy cannot be created or destroyed, only transformed. When a ball is dropped, it has potential energy due to its position above the ground. As it falls, this potential energy is converted into kinetic energy, resulting in an increase in velocity. When the ball hits the ground, some of this kinetic energy is converted into other forms of energy, such as heat and sound, causing the velocity to decrease.

What factors affect the velocity of a ball when it hits the ground?

The velocity of a ball when it hits the ground can be affected by several factors. These include the initial height of the ball, the gravitational acceleration, the air resistance, and the elasticity of the ball and the ground. A higher initial height and a lower air resistance will result in a higher velocity upon impact, while a lower gravitational acceleration and a more elastic collision between the ball and the ground will result in a lower velocity.

Can the velocity of a ball when it hits the ground be greater than its initial velocity?

Yes, the velocity of a ball when it hits the ground can be greater than its initial velocity. This can occur if the ball has a high initial height and/or a low air resistance. In these cases, the ball will have a higher velocity upon impact due to the conversion of potential energy into kinetic energy. However, the velocity of the ball cannot be greater than the speed of light, as this violates the laws of physics.

What is the relationship between the velocity of a ball and the time it takes to hit the ground?

The relationship between the velocity of a ball and the time it takes to hit the ground can be described by the equation: v = gt, where g is the gravitational acceleration and t is the time. This equation assumes no air resistance and a constant gravitational acceleration. It shows that the velocity of the ball increases as the time increases, and it is directly proportional to the gravitational acceleration. Therefore, the longer the ball falls, the higher the velocity will be when it hits the ground.

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