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Chapter 3: Problem 10

You're in a bus moving with constant velocity on a level road when you throw a ball straight up. When the ball returns, does it land ahead of you, behind you, or back at your hand? Explain.

Short Answer

Expert verified
The ball lands back in your hand. This is based upon principles of relative motion and the fact that no horizontal forces act on the ball during its flight, given that the bus does not change speed or direction during the course of the ball's flight.

Step by step solution

01

Evaluate the initial condition

The bus is moving with a constant speed and you are also moving with the same speed as the bus. So, when you throw the ball up, it is thrown not from a stationary position but from a moving one. The ball takes this initial horizontal velocity with it according to the principles of relative motion.
02

Consider the motion of the ball

The moment the ball leaves your hand, it has two components of movement -- upwards (opposed by gravity) and forwards (due to its initial horizontal velocity). The key point is that there is no force acting horizontally on the ball (we neglect air resistance) after it is thrown. Thus, it maintains its horizontal speed throughout its motion.
03

Consider the landing of the ball

Because the ball had the same horizontal velocity as the bus (and you) when it was thrown and continues to maintain it during the flight upwards and downwards (due to no horizontal forces acting on it), it will land back in your hand, assuming the bus does not change speed or direction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Constant Velocity
When we talk about an object moving with a constant velocity, it means that the object is travelling at the same speed and in the same direction without changing. This implies there is no acceleration or deceleration, and the path remains straight.

In the bus example, both you and the ball maintain a constant velocity in the horizontal direction, which is the same as that of the bus. This is because there are no external forces present to change the ball's speed or direction once it leaves your hand. Understanding this will clarify why, when you throw the ball straight up in the air, it doesn’t just go up and down vertically but also maintains a forward motion.
Principles of Relative Motion
The principles of relative motion play a crucial role when analyzing the movement of objects from different reference frames. Relative motion is the calculation of the motion of an object as observed from another moving object.

From your viewpoint within the bus, which is a moving reference frame, the ball seems to only move vertically. However, for an outside observer, the ball will trace a parabolic path, as it inherits the bus's constant horizontal velocity. Grasping this concept is essential to predict where the ball will land if you are on a moving vehicle—or indeed, if you are moving along with any object.
Components of Movement
Objects in motion often have components of movement in more than one direction. In our bus example, the ball has two primary components of motion once it leaves your hand: the vertical component, due to the force you apply upwards, and the horizontal component, which is the same as the constant velocity of the bus.

This illustrates how movements in different directions can be independent of one another. In a motion where multiple components are involved—like the ball’s path in the moving bus—it is the individual components that combine to describe the complete motion.
Neglecting Air Resistance
When we consider problems in physics that include any kind of projectile or object in flight, simplifying assumptions are often made. One such simplification is neglecting air resistance.

In reality, air resistance applies a force opposite to the direction of movement and is dependent on factors like the object's velocity, surface area, and shape. However, for the sake of simplicity and focusing on key concepts, we often assume it to be negligible. This allows us to concentrate on the effects of gravity and any initial velocities the object may have, giving us a more straightforward understanding of the ball's trajectory in our bus scenario.
Horizontal Velocity
The concept of horizontal velocity is particularly useful when dealing with projectiles or objects in motion within a horizontal plane. It refers to the component of an object’s velocity that runs parallel to the Earth's surface.

In our example, the bus and anything inside it, like the ball at the moment it's released, have a horizontal velocity. The crucial point here is that unless acted on by another force, the horizontal velocity will remain constant due to Newton's first law of motion, often referred to as the law of inertia. This law explains why the ball doesn’t fall behind or land ahead of you but instead returns to your hand.

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Most popular questions from this chapter

A projectile launched at angle \(\theta\) to the horizontal reaches maximum height \(h .\) Show that its horizontal range is \(4 h /\) tan \(\theta\)

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