Physics 103: Physics for Life Sciences I
Growth Speed
Name______________________________________________
The images of trees in the figure come from a catalog of fast growing trees. If we mark
the position of the top of the tree in the successive years, as shown in the graph in the
figure, we obtain a motion diagram much like the ones we have seen for other kinds of
motion. The motion isn’t steady, of course. In some months the tree grows rapidly; in
other months, quite slowly. We can see, though, that the average speed of growth is fairly
constant for the first few years.
What is the tree’s speed of growth, in feet per year from 1 – 3 years?
What is the speed in meters per second?
At the end of year 3, a rope is tied to the very top of the tree to steady it. This rope is
staked into the ground 15 feet away from the tree. What angle does the rope make with
the ground?
Physics 103: Physics for Life Sciences I
Position, Velocity and Acceleration Graphs
Name______________________________________________
For each of the following situations, show what the position/time,
velocity/time, and acceleration/time graphs look like.
a. The man starts three meters from the house and accelerates towards a tree.
b. The man stands still while he talks on his cell phone at the middle of the sidewalk, then
walks toward the house at a constant rate trying to get better cell reception. He comes to a
sudden stop when the coverage is good (about a meter before the house) and stands still
to finish his conversation.
c. The man starts close to the house, stands still for a little while, then walks toward the
tree at a constant rate for a while, then the slows to a stop.
Physics 103: Physics for Life Sciences I
Free Fall on Different Worlds
Name______________________________________________
Objects in free fall on the earth have acceleration of -9.8 m/s2. On the moon, free fall
acceleration is approximately 1/6 of the acceleration on earth. This changes the scale of
problems involving free fall. For instance, suppose you jump straight upward, leaving the
ground with velocity vi and then steadily slowing until reaching zero velocity at your
highest point. Because your initial velocity is determined mostly by the strength of your
leg muscles, we can assume your initial velocity would be the same on the moon.
If an astronaut can jump straight up to a height of 0.50 m on earth, how high could he
jump on the moon?
On the earth, an astronaut can safely jump to the ground from a height of 1 m, her
velocity when reaching the ground is slow enough not to cause injury. From what height
could the astronaut safely jump to the ground on the moon?
An astronaut drops three balls in equal time intervals such that the third ball is released
when the first ball hits the ground. If the height the balls are dropped is 1.2m, how high is
the second ball from the ground upon the third ball released? Is this distance 0.6m, closer
to the ground or release point, explain.
Physics 103: Physics for Life Sciences I
The Chase
Name______________________________________
Cheetahs have the highest top speed of any land animal, but they usually fail in their
attempts to catch their prey because endurance is limited. They can maintain their
maximum speed of 30 m/s for only about 15 s before they need to stop.
Thomson’s gazelles, their preferred prey, have a lower top speed than cheetas, but they
can maintain this speed for a few minutes. When a cheetah goes after a gazelle, success
or failure is a simple matter of kinematics: Is the cheetah’s high speed enough to allow it
to reach its prey before the cheetah runs out of steam? The following problem uses
realistic data for such a chase.
A cheetah has spotted a gazelle. The cheetah leaps into action, reaching its top speed of
30 m/s in a few seconds. At this instant, the gazelle, 160 m from the running cheetah,
notices the danger and heads directly away. The gazelle accelerates at 4.5 m/s2 for 6.0 s,
then continues running at a constant speed. After reaching its maximum speed, the
cheetah can continue running for only 15 s. Does the cheetah catch the gazelle, or does
the gazelle escape?
(a) How far does the cheetah travel during this 15 s duration?
(b) How far does the gazelle travel during the entire duration?
(c) Who is ahead at the end of 15 seconds? Does the cheetah catch the gazelle, or does
the gazelle escape?