PhysicsLAB Resource Lesson
Freefall: Horizontally Released Projectiles (2D-Motion)

When a projectile is released with a non-zero horizontal velocity, its trajectory takes on the shape of a parabola. There are now two dimensions to its motion: 
 
  • Vertically, gravity is still accelerating it at -9.8 m/sec2
  • Horizontally, there is no acceleration since gravity acts at right angles to that velocity's component.
 
Consequently, the trajectory must be analyzed in two parts.

Horizontally, the projectile travels at a constant velocity. Gravity acts perpendicularly to the projectile's horizontal component and therefore does not produce any linear acceleration. In the following diagram, the fact that the horizontal velocity remains constant is indicated by the equally spaced dots across the top. Vertically, the projectile is accelerating towards the center of the earth at the rate of 9.8 m/sec2. This uniform acceleration is indicated by the fact that the vertical dots have an ever-increasing separation. As a direct consequence of the equation s = vot + ½ at2, the vertical spacing between dots increases by odd integers.
 
 
 
When a projectile is released completely horizontally, then we start with the following conditions:
 


Horizontal motion
Vertical motion
time
a = 0 a = - 9.8 m/sec2
v = vH vo = 0
R = vHt s = vot + ½at2
 
In this table, the variable, R, represents the range of the projectile, or the horizontal distance that the projectile travels from the point of release until it strikes the ground.  Note that the time, crosses between the components. That is, time is a parameter that applies to both columns - a common quantity.
 
Refer to the following information for the next five questions.

While standing on an elevated balcony, a child tosses a penny horizontally at 3 m/sec from its railing. The penny lands on the ground floor 1.5 seconds later.
 How high is the balcony above the ground floor?

 If he tossed the coin at horizontally 3 m/sec, what was the penny's range?

 How fast was the penny traveling horizontally when it struck the ground floor?

 How fast was it travelling vertically when it struck the floor?

 Was any point in the penny's trajectory ever higher than the balcony's railing?

Refer to the following information for the next four questions.

While standing on a 30 meter bridge, a fisherman tosses some unused bait off the bridge. He releases it horizontally at 3 m/sec.
 How long does the bait take to hit the water under the bridge?

 How fast is it traveling horizontally when it strikes the water?

 How fast is it traveling vertically when it strikes the water?

 What is its range? That is, how far does it travel horizontally before striking the water?





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