If a ball is thrown up into the air, the equation for its position is:
where…
is the height—given as a function of time, of course—measured in feet.
is the time, measured in seconds.
is the initial height that it had when it was thrown—or, to put it another way,
is height when
.
is the initial velocity that it had when it was thrown, measured in feet per second—or, to again put it another way,
is the velocity when
.
This is sometimes called the
equation of motion for an object, since it tells you where the object is (its height) at any given time.
Use that equation to solve the questions below.
I throw a ball up from my hand. It leaves my hand 3 feet above the ground, with a velocity of 35 feet per second. (So these are the
initial height and velocity,
and
.)
Write the equation of motion for this ball. You get this by taking the general equation I gave you above, and plugging in the specific
and
for this particular ball.
How high is the ball after two seconds? (In other words, what
value do you get when you plug in
?)
What
value do you get when you plug
into the equation? Explain in words what this result means.
I throw a different ball, much more gently. This one also leaves my hand 3 feet above the ground, but with a velocity of only 2 feet per second.
Write the equation of motion for this ball. You get this by taking the general equation I gave you above, and plugging in the specific
and
for this particular ball.
How high is the ball after two seconds? (In other words, what
value do you get when you plug in
?)
What
value do you get when you plug
into the equation? Explain in words what this result means.
