## 1008 Stones thrown vertically upward | Rectilinear Translation

## 1007 Finding when and where the stones pass each other | Rectilinear Translation

**Problem 1007**

A stone is dropped from a captive balloon at an elevation of 1000 ft (304.8 m). Two seconds later another stone is thrown vertically upward from the ground with a velocity of 248 ft/s (75.6 m/s). If g = 32 ft/s^{2} (9.75 m/s^{2}), when and where the stones pass each other?

## 1005 Finding the depth of well by dropping a stone | Rectilinear Translation

**Problem 1005**

A stone is dropped down a well and 5 sec later, the sounds of the splash is heard. If the velocity of sound is 1120 ft/sec (341.376 m/s), what is the depth of the well?

## 1004 Relative velocity | Rectilinear Translation

**Problem 1004**

A ball is dropped from the top of a tower 80 ft (24.38 m) high at the same instant that a second ball is thrown upward from the ground with an initial velocity of 40 ft/sec (12.19 m/s). When and where do they pass, and with what relative velocity?

## 1003 Return in 10 seconds | Rectilinear Translation

**Problem 1003**

A stone is thrown vertically upward and return to earth in 10 sec. What was its initial velocity and how high did it go?

## 1002 Location of warning torpedo | Rectilinear Translation

**Problem 1002**

On a certain stretch of track, trains run at 60 mph (96.56 kph). How far back of a stopped train should be a warning torpedo be placed to signal an oncoming train? Assume that the brakes are applied at once and retard the train at the uniform rate of 2 ft/sec^{2} (0.61 m/s^{2}).

## Curvilinear Translation (Projectile Motion)

Projectile motion follows a parabolic trajectory. The vertical component of projectile is under constant gravitational acceleration and the horizontal component is at constant velocity. For easy handling, resolve the motion into x and y components and use the formulas in rectilinear translation.

Form the figure below:

$v_{oy} = v_o \, \sin \theta$

## Kinematics

**Motion of a Particle**

Particle is a term used to denote an object of point size. A system of particles which formed into appreciable size is termed as body. These terms may apply equally to the same object. The earth for example may be assumed as a particle in comparison with its orbit, whereas to an observer on the earth, it is a body with appreciable size. In general, a particle is an object whose size is so small in comparison to the size of its path.

**Rectilinear Translation (Motion Along a Straight Line)**

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## Dynamics

**Dynamics** is the branch of mechanics which deals with the study of bodies in motion.

**Branches of Dynamics**

Dynamics is divided into two branches called *kinematics* and *kinetics*.

Kinematics is the geometry in motion. This term is used to define the motion of a particle or body without consideration of the forces causing the motion.

Kinetics is the branch of mechanics that relates the force acting on a body to its mass and acceleration.

**Symbols and Notations**

s = distance

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