Honors Physics Scrapbook
1.
Title: A Snowball as a Free-Falling Object
Picture: a rubber ball being tossed upward by a man standing on a platform
A free-falling object is an object that is falling under the sole influence of gravity. All
free-falling objects (on Earth), including the baseball illustrated in the picture above,
have a constant acceleration of -9.80 m/s
2
, no matter if they are thrown upwards or
downwards
(accelerate downwards at a rate of -9.80 m/s
2
). When the rubber ball is
tossed upward, its initial velocity is positive, and its acceleration, once it’s in the air, is
-9.8 m/s
2
. The rubber ball will slow down as it rises, and will have a velocity of 0 m/s
at the peak of its trajectory. Furthermore, because the rubber ball is tossed vertically
upwards, the velocity at which it is thrown will have the opposite sign of the velocity
that it has when it returns to the same height it was thrown (for example, if the rubber
ball is thrown vertically upwards with a velocity of 30 m/s, it will have a velocity of -30
m/s when it returns to the same height it was thrown). Similarly, if the rubber ball is
thrown downwards, its acceleration is also -9.8 m/s
2
. The ball’s initial velocity,
however, if it is simply dropped from a certain height, will be 0 m/s. Generally when
objects are in the state of free-fall, air resistance force is neglected.
Problem: A ball is thrown from the top of a building at a speed of 5.6 m/s. The height
of the building is 40.0 m. How long does it take the ball to reach its maximum height?
Givens:
Two equations:
v
0
= 5.6 m/s
v = at + v
0
∆t = ?
∆d = v
0
∆t + 0.5a(∆t)
2
∆a = -9.80 m/s
2
∆d = 40.0 m
1) v = (-9.80 m/s
2
)t + 5.6 m/s
Substitute v=0, the velocity at maximum height, into
2) ∆d = (5.6 m/s)t – 0.5(9.80 m/s
2
)t
2
Equation (1) and solve for time:
∆d = (5.6 m/s)t – (4.90 m/s
2
)t
2
0 = (-9.80 m/s
2
)t + 5.6 m/s
-5.6 m/s = (-9.80 m/s
2
)
t = -5.6 m/s
-9.80 m/s
2
t = 0.5714 s
2.
Title: Throwing a Baseball, An Example of Projectile Motion
Picture: a person throwing a baseball at his/her friend who is catching it
Projectile motion is a type of two-dimensional motion that pertains to objects that
move in both the x- and y-directions simultaneously under constant acceleration. In
projectile motion, no matter how the objects enter the air, once they are in the air,
they are under the sole influence of gravity. Since gravity only acts in the y-direction,
the y-component is the only one that changes. Thus, the x-velocity remains constant
while the y-velocity changes as it would in a free-falling state. Similarly, in the picture
above, only the baseball’s y-velocity and y-component motion change. The baseball’s
x-component of the velocity, v
x
, remains constant in time, meaning that it is equal to
its initial velocity, v
0x
. As the baseball travels in its parabolic trajectory, v changes with
time, and the y-component of the velocity is zero at the peak of the trajectory. Finally,
the acceleration, which acts downward, of the baseball, is always equal to the
acceleration that the baseball has in a free-falling state.