Kinematics of rolling ball question

In summary, the problem involves a ball rolling off a table at a height of 1.225 m and a speed of 6 m/s, and the goal is to determine how long it will take for the ball to hit the ground. The correct equation to use is Distance = Vo + 1/2at^2, where the initial vertical velocity (Vo) is 0. The horizontal velocity does not affect the vertical displacement, so it can be ignored.
  • #1
Bionerd
12
0

Homework Statement



Hello, new here. I'm doing homework for my Honors Physics class, and I have a kinematics problem that seems simple enough, but I just can't get it. Help, please?

A ball is rolling on a table 1.225 m high at 6 m/s. After it rolls off, how long does it take to hit the ground?


Homework Equations



I used V^2= (Vo)^2 + 2a(X-Xo) to find final velocity, than used V= Vo+at to find time.


The Attempt at a Solution



V^2= (6 m/s)^2 + 2(9.8 m/s^2)(1.225 m) V= 7.7 m/s

t= (V-Vo)/a = (7.7 m/s - 6 m/s)/ 9.8 m/s^2 t= .17 s

I know this is wrong. My physics teacher told me to use Vx, not Vy, for Vo. I'm not quite sure how to go about this. Do I need to find the angle (which I'm not sure how to do in this problem) and use Vox= Vocos(theta)?

Any help would be appreciated. :redface:
 
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  • #2
On the table the ball only had a horizontal velocity... that only affects horizontal displacement... it doesn't affect vertical displacement.

What is the initial vertical velocity? You have a vertical displacement of -1.225m.
 
  • #3
It doesn't matter what the horizontal velocity is, the 6m/s is there to confuse you. Only consider the vertical motion, Use Distance= Vo + 1/2at^2 where Vo (the initial vertical velocity) is 0. Oh, and only consider the distance traveled to be negative if you consider the acceleration to be negative.
 

1. What is the definition of kinematics?

Kinematics is the study of motion, including the position, velocity, and acceleration of objects, without considering the forces that cause the motion.

2. How is kinematics applied to a rolling ball?

Kinematics can be used to analyze the motion of a rolling ball by considering its position, velocity, and acceleration over time. This can help determine factors such as the distance traveled, speed, and direction of the ball.

3. What is the equation for calculating the velocity of a rolling ball?

The equation for calculating the velocity of a rolling ball is v = ωr, where v is the velocity, ω is the angular velocity, and r is the radius of the ball.

4. How does the shape and size of a rolling ball affect its kinematics?

The shape and size of a rolling ball can affect its kinematics by changing its moment of inertia, which in turn affects its angular velocity and acceleration. A larger or more irregularly shaped ball will have a higher moment of inertia and therefore require more force to achieve the same acceleration as a smaller or more symmetrical ball.

5. What are some real-life applications of kinematics of a rolling ball?

The kinematics of a rolling ball can be used in various real-life applications, such as designing and analyzing the motion of wheels in vehicles, predicting the trajectory of a rolling ball in sports like bowling or golf, and understanding the motion of objects in machinery and robotics.

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