# Solving Stick Thrown in Air with Initial Condition

• Tanya Sharma
In summary, a student throws a stick of length L up into the air with a speed of 0 at the closest end. The stick completes N turns and is caught by the student at the initial release point. The problem involves finding the height 'h' that the center of mass rises. The relevant equation is v=ωr and the initial orientation of the stick is horizontal.
Tanya Sharma

## Homework Statement

A student throws a stick of length L up into the air.At the moment it leaves her hand the speed of stick's closest end is zero.The stick completes N turns just as it is caught by student at initial release point.What is the height 'h' that center of mass rise ?

v=ωr

## The Attempt at a Solution

I think I can proceed with the problem but feel a little unsure about the initial orientation of the stick just as it leaves the hand and the initial condition that the the speed of stick's closest end is zero .

Could somebody reflect on how to interpret the initial condition given in the problem ?

Thanks

I would think that if the centre of mass was to go up, the only way that the point nearest the hand could be moving relative to it would be downwards in order for it to be stationary. I.e. Not left or right.

Do you mean the stick is horizontal at the instant it leaves the hand ?

See figure.

ehild

#### Attachments

• thrownstick.JPG
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Hi ehild...

Someone has rightly said "A picture is worth a thousand words " .

Thanks...

## 1. What is the initial condition in solving stick thrown in air?

The initial condition in solving stick thrown in air is the initial position and velocity of the stick when it is thrown into the air. This includes the height from which the stick is thrown, the angle at which it is thrown, and its initial velocity.

## 2. How do you calculate the trajectory of a stick thrown in air?

The trajectory of a stick thrown in air can be calculated using the equations of motion and the initial conditions of the stick. This involves using the equations for displacement, velocity, and acceleration to determine the stick's position at any given time.

## 3. What factors affect the trajectory of a stick thrown in air?

The trajectory of a stick thrown in air is affected by several factors, including the initial conditions of the throw, air resistance, and the gravitational force. The shape, size, and weight of the stick can also impact its trajectory.

## 4. How can air resistance be accounted for in solving stick thrown in air?

Air resistance can be accounted for in solving stick thrown in air by using the drag force equation and including it in the equations of motion. The drag force is dependent on the shape and size of the stick, as well as the air density and velocity.

## 5. Can the trajectory of a stick thrown in air be affected by external factors?

Yes, external factors such as wind, temperature, and air density can affect the trajectory of a stick thrown in air. These factors can cause changes in the drag force and gravitational force, altering the stick's trajectory. Other factors such as the stick hitting an object or changing direction mid-flight can also affect its trajectory.

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