# Laws of Motion- dropping book off building with a twist

• a.k
In summary, we are given a physics book of mass 2.0kg dropped from a building 240.1m high with a horizontal wind force of 11N acting on it. We are asked to find the distance from the building when it hits the ground, the time it takes to hit the ground, and the speed at which it hits the ground. Using the equations ay=-g=-9.8m/s^2 and ax=force of the wind/m, we can calculate the horizontal acceleration to be 5.5m/s^2. Using this, we can then solve for part a, finding the distance from the building to be 134.75m. For part b, we use the equation t=sqrt
a.k

## Homework Statement

A 2.0kg physics book is dropped from the roof of a skyscraper 240.1 m high. While the book is falling to the ground, a horizontal wind exerts a constant force of 11 N on it. Ignore air resistance.

a. How far from the building is the book when it hits the ground?
b. How long does it take the book to hit the ground?
c. What is the speed of the book when it hits the ground?

## Homework Equations

ay=-g=-9.8m/s^2
ax=force of the wind/m

## The Attempt at a Solution

Using the second formula,

11N/2kg=5.5 m/s^2

I would like some advice as to what to do now.

Ok, I figured out some more info. on this problem.

For part b,

t=sqrt(2y/ay)

2*-240.1

sqrt(49)

t=7 secs

a.k said:
Ok, I figured out some more info. on this problem.

For part b,

t=sqrt(2y/ay)

2*-240.1

sqrt(49)

t=7 secs
Good. Now use the horizontal acceleration you calculated to solve part a.

So part a,

x=1/2axt^2

1/2(5.5)(7)^2
269.5/2
x=134.75 m

Im not sure if using "x" is correct. It is suppose to show horizontal accel, so ax?

a.k said:
So part a,

x=1/2axt^2

1/2(5.5)(7)^2
269.5/2
x=134.75 m
Good.

Im not sure if using "x" is correct. It is suppose to show horizontal accel, so ax?
Calling the horizontal component of acceleration ax is fine.

Ok I am working on part c and ax is actually 5.5 m/s^2. I am confusing myself.

a.k said:
Ok I am working on part c and ax is actually 5.5 m/s^2. I am confusing myself.
Find the vertical and horizontal components of the velocity when it hits the ground.

Vy=ayt
Vx=axt

Vy=-68.6 m/s
Vx=38.5 m/s

V=sqrt(38.5^2+-68.6^2)
sqrt(6188.21)
V=78.67 m/s

Good job!

## 1. What is Newton's First Law of Motion?

Newton's First Law of Motion, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will continue in motion with a constant velocity unless acted upon by an external force.

## 2. How does dropping a book off a building with a twist relate to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In the case of dropping a book off a building with a twist, the force of gravity pulling the book towards the ground is the net force and the mass of the book affects the acceleration of the book as it falls.

## 3. What is the relationship between the height and time it takes for the book to hit the ground?

The relationship between the height and time it takes for the book to hit the ground is described by Newton's Law of Universal Gravitation. This law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. As the book falls from a greater height, the distance between the book and the ground decreases, resulting in a stronger gravitational force and a shorter time for the book to hit the ground.

## 4. How does air resistance affect the motion of the falling book?

Air resistance, also known as drag, acts in the opposite direction of the motion of the falling book. This force increases as the speed of the book increases. As a result, air resistance will slow down the book's acceleration towards the ground, making it take longer to reach the ground compared to if it were falling in a vacuum.

## 5. Can the book's trajectory be affected by the twist in this experiment?

Yes, the twist can affect the book's trajectory. If the twist is applied in a way that creates a lift force, it can counteract some of the force of gravity pulling the book downwards. This can result in the book taking longer to reach the ground or even changing its trajectory slightly.

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