Question

An object of mass m is projected horizontally from the top of a

building. The object's initial velocity is v, its initial height is H, and it travels
a horizontal distance D before striking the ground. Let represent the time
that the object is a projectile.
(a) Write two equations that relate the quantities v, H, D, t, and fundamental
constants.
H

Answer 1

The principles of projectile motion involve two main equations: one for horizontal motion (D = vt) and another for vertical motion under gravity (H = ½gt²). With these equations, variables like time, distance, and initial velocity can be interrelated and calculated accordingly.

Step-by-step explanation:

The question deals with the principles of projectile motion, specifically regarding an object that is projected horizontally from a height. In such cases, there are two primary equations used to relate the variables:

• The equation for horizontal motion: D = vt, where D represents the horizontal distance traveled, v is the initial horizontal velocity, and t is the time the object is in the air.
• The equation for vertical motion under constant acceleration due to gravity: H = ½gt², where H is the initial height from which the object is projected, g is the acceleration due to gravity (9.81 m/s² on Earth), and t is the time the object is in the air.

Using these equations, you can solve for one variable if the others are known. For example, to determine the time t the object is in the air, you would rearrange the second equation to solve for t:

t = √(2H/g)