e-throw

Projectile Motion – Let’s Explore Different Types of Projectile Motion!

Velocity Vector Acceleration Vector 　　Horizontal Vertical
Lunar Surface [ Monkey Catch - Relative Direction - Monkey Position ] Air Resistance 　

* By dragging the top-right slider, you can change the vertical position of the origin (0), as well as the magnitude and direction of the velocity vector (its tip).

Description :
    This is a page for investigating the motion of projectile objects under various conditions.
    Let’s examine the motion of an object under uniform gravity in the downward direction. The motion of an object in uniform gravity is uniformly accelerated motion, with vertical motion represented as uniformly accelerated linear motion, and horizontal motion as uniform linear motion. This type of motion generally traces a parabolic trajectory, which is a quadratic curve.
    The acceleration due to gravity is called gravitational acceleration, and its magnitude is 9.8 meters per second squared at the Earth's surface, independent of mass. This occurs because gravity is proportional to mass, but acceleration is inversely proportional to mass according to the equations of motion. As a result, the gravitational acceleration remains constant, regardless of the object's mass. On the Moon, the gravitational acceleration is about one-sixth of Earth's, at 1.62 meters per second squared, so the falling motion is different.
    Now, let's investigate a problem called "Monkey Catch." If a monkey lets go of a tree branch and starts free falling at the same time an apple is thrown towards it, think about the conditions under which the monkey will successfully catch the apple and why this happens. ("Monkey Catch" might actually be more commonly referred to as "Monkey and Hunter".)
    Also, on Earth, air resistance exists, which affects motion. In fast-moving cases like a baseball hit, air resistance is dominated by inertia drag and works in the opposite direction to velocity, proportional to the square of the speed, causing a deviation from the ideal parabolic trajectory. Furthermore, when the resistance is large, the velocity eventually reaches terminal velocity, and the motion becomes a steady fall at that constant speed.
    Let's confirm these types of motions through simulations.

● The arrow from the object represents the velocity vector, and you can change the magnitude and direction of the initial velocity by dragging.
● You can adjust the magnitude of the initial velocity and the angle from the horizontal by dragging the slider in the top-right corner.
● By dragging near the origin (red), you can move the origin up or down.
● The "Start/Stop" button allows you to launch the object and control the progression or stopping of time.
● The "Slow/Stop" button lets you observe the motion of the object in slow motion.
● The "0" button resets the time to zero. Be sure to press this button if you want to try again.
● The "Reset" button returns everything to its initial state.
● The checkboxes "Acceleration Vector" and "Velocity Vector" allow you to display the respective vectors.
● The "Horizontal" checkbox displays an object moving with uniform horizontal motion, while the "Vertical" checkbox shows an object undergoing uniformly accelerated linear motion due to gravity.
● The "Moon" checkbox adjusts the gravity to that of the Moon's gravitational acceleration.
● The "Monkey Catch." and "Relative Direction" checkboxes let you explore the Monkey Catch problem. The brown circle represents the monkey. The "Monkey Position" slider can adjust the horizontal position of the monkey.
● The air resistance slider allows you to apply air resistance. The larger the value, the greater the air resistance force. For comparison, the motion without air resistance is represented by a small pink ball.

Back to Contents Page