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/s2 (9.75 m/s2), when and where the stones pass each other?

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:

$v_{ox} = v_o \, \cos \theta$

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





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)


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