Horizontally Launched Projectile
Problems
One of the powers of physics is its ability to use physics
principles to make predictions about the final outcome of a moving object. Such
predictions are made through the application of physical principles and
mathematical formulas to a given set of initial conditions. In the case of
projectiles, a student of physics can use information about the initial
velocity and position of a projectile to predict such things as how much time
the projectile is in the air and how far the projectile will go. The physical
principles that must be applied are those discussed
previously in Lesson 2. The
mathematical formulas that are used are commonly referred to as kinematic
equations. Combining the two allows one to make predictions concerning the
motion of a projectile. In a typical physics class, the predictive ability of
the principles and formulas are most often demonstrated in word story problems
known as projectile problems.
There are two basic types of projectile problems that we will
discuss in this course. While the
general principles are the same for each type of problem, the
approach will vary due to the fact the problems differ in terms of their
initial conditions. The two types of problems are:
A projectile is launched with an initial horizontal velocity
from an elevated position and follows a parabolic path to the ground.
Predictable unknowns include the initial speed of the projectile, the initial
height of the projectile, the time of flight, and the horizontal distance of
the projectile.
Examples of this type of problem
are
a. A pool
ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4
m/s. Predict the time required for the pool ball to fall to the ground and the
horizontal distance between the table's edge and the ball's landing location.
b. A soccer
ball is kicked horizontally off a 22.0-meter high hill and lands a distance of
35.0 meters from the edge of the hill. Determine the initial horizontal
velocity of the soccer ball.
A projectile is launched at an angle to the horizontal and
rises upwards to a peak while moving horizontally. Upon reaching the peak, the
projectile falls with a motion that is symmetrical to its path upwards to the
peak. Predictable unknowns include the time of flight, the horizontal range,
and the height of the projectile when it is at its peak.
Examples of this type of problem are
a. A football
is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the
horizontal. Determine the time of flight, the horizontal distance, and the peak
height of the football.
b. A long
jumper leaves the ground with an initial velocity of 12 m/s at an angle of
28-degrees above the horizontal. Determine the time of flight, the horizontal
distance, and the peak height of the long-jumper.
The second problem type will be the subject of the next
part of Lesson 2. In this part of Lesson 2,
we will focus on the first type of problem - sometimes referred to as
horizontally launched projectile problems.
Three common kinematic equations that will be used for both type of problems
include the following:
d = vi•t + 0.5*a*t2
vf = vi + a•t
vf2 = vi2 + 2*a•d
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where |
d = displacement |
a = acceleration |
t = time |
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vf = final velocity |
vi = initial velocity |
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