How Do You Calculate the Initial Velocity of a Juggling Ball?

[c.kal]

You are practicing your juggling skills by throwing a single juggling ball back and forth between level hands. The distance between your hands is 40 cm. Between catches, the ball is in the air 0.85 s. Calculate the magnitude and direction of initial velocity of the juggling ball each time you throw it.

i'm not sure where to start on this one..

 

[NascentOxygen]

Hi c.kal, I see you are new here. http://imageshack.com/a/img515/4884/welcomesign.gif

You start this problem the same way as you start any physics problem---you write down what you are given and what you are required to find. This includes a sketch because things are clearer if you have some pictorial aid to focus on. Then you write down as many relevant equations as you can. Next, cross out those equations that you can see are of no use here.

Then, you get serious ...

 

[c.kal]

I sketched and labeled it but I still can't figure out where to start

 

[NascentOxygen]

Post what you've done here. Show the kinematics equations that might be useful.

Hint: when a ball thrown into the air returns to the level it was thrown from, its displacement at that point equals zero.

 

[HalfLostAndSearching]

I would approach this problem by using principles of projectile motion and kinematics to analyze the motion of the juggling ball. Projectile motion refers to the motion of an object that is launched into the air and moves in a curved path under the influence of gravity.

In this scenario, we can assume that the juggling ball is being thrown with an initial velocity in a horizontal direction and is experiencing a constant acceleration due to gravity in the vertical direction. The distance between the hands, 40 cm, can be considered the horizontal displacement of the ball.

To calculate the initial velocity, we can use the equation v = d/t, where v is the velocity, d is the displacement, and t is the time. In this case, the displacement is 40 cm and the time is 0.85 s. Therefore, the initial velocity of the juggling ball each time it is thrown is approximately 47.06 cm/s.

As for the direction of the initial velocity, we can use the concept of vector components. Since the ball is being thrown horizontally, the initial velocity will only have a horizontal component. This means that the direction of the initial velocity will be in the same direction as the displacement, which is from one hand to the other.

In conclusion, the magnitude of the initial velocity of the juggling ball is 47.06 cm/s and the direction is horizontal, from one hand to the other. By understanding the principles of projectile motion, we can analyze and calculate the motion of objects in various scenarios, such as juggling, and better understand the physical world around us.