**A
football is kicked into the air with an initial upward velocity of 25 meters per
second. (m/sec)
**

**Calculate
it's height after 2 seconds.**

**Calculate
it's height after 3 seconds.**

**When
will it be 20 meters above the ground?**

**When
will the ball hit the ground?**

**A
twirler throws a baton with an initial upward velocity of 20 meters per second
(m/sec).
**

**Calculate
it's height after 2 seconds.
**

**When
will it be 15 meters above where it was thrown?**

**When
will the baton be back at the twirler's level?**

**Milt
Famey, the baseball player, hits a pop fly to the infield. It goes upward with
an initial velocity of 30 (m/sec).
**

**What
is the altitude after 2 seconds?
**

**When
is it 25 meters above where it was hit?
**

**When
is it back down?
**

**The
ball is at it's highest halfway between the time it was hit (t=0) and the time
it gets back down. (see part c)
**

**When
is it at it's highest?**

**The
ball will be at his highest at 3 seconds. (1/2 of 6)**

**What
is it's highest distance?**

A
cannonball is fired with an initial upward velocity of 100m/s.

**Calculate
it's altitude after 3 seconds.**

**At
what times will it be 480 meters high?**

**When
does it return to the ground?**

**The
cannonball reaches it's highest point halfway between the time it is fired
(t=0)and the time it hits the ground.
**

**When
will it reach it's highest?**

**How
high is it at it's highest?**

**Snoopy
is flying in his Sopwith Camel. He fires at the Red Barron.
The bullet has an upward initial velocity of 120m/sec.
**

**The
Red Barron is 400 meters above Snoopy. When will the bullet first reach his
altitude?**

**The
bullet misses on the way up. Could it hit the Red Barron on it's way back down?**

**If
the bullet also misses the Red Barron on it's way down, will it be back at the
level with Snoopy's Sopwith Camel?**

**If
it misses Snoopy on the way down, when will it hit the ground, 900 meters below
where it was fired?**

**Suppose that you throw a rock into the air from the top of
a cliff. The initial upward velocity is 15 (m/sec).**

**How high will the rock be above the cliff top after 2
seconds?**

**Where will it be after 4 seconds?**

**When will it again be at the same level you threw it?**

**When will it hit the water, 50 meters below where you
threw it?**

**At the circus, Art Tillery is fired into the air from a
cannon on a platform. His initial upward velocity is 7m/sec.**

**How high is he above the firing point after 0.6 seconds?**

**When will be 2 meters above his firing point?**

**When will he be back at the level of the cannon?**

**When will he land in the tank of water, 20 meters below
his firing point?**

**8.
Coyote and Roadrunner Problem**

**Wile E. Coyote is standing on a springboard atop the high
cliff. Roadrunner drops a boulder on the other end of the springboard, sending
Wile up with an initial velocity of 45m/sec.**

**How high will Wile be after 4 seconds?**

**At what other time will he be the same altitude as above?**

**At 4 seconds, was Wile going up or down?**

*Going up since he was at 100 meters later, at 5
seconds, going down.*

**When does he reach the level of the springboard?**

**On the way down, Wile misses the cliff. At what time does
he land in the river 120 meters below the top of the cliff?**

**Chuck throws a rock with an initial upward velocity of
12m/sec.**

**How high is it after 0.7 seconds?**

**When will it be 7.2 meters up?**

**At the time in the problem above, is it going up or down?**

*It was neither going up nor down. It had reached its
high point since there was only one value of t.*

**When does the rock get back to the ground level?**

**On the way down, the rock goes straight down a well,
splashing at the bottom 4 seconds after it was thrown. How deep is the well?**

**As Al Pine jumps off the end of a ski jump, he has an
initial velocity of 13 meters/second.**

**How high will he be 2 seconds after he jumps?**

**At what other time will he be as in the problem above?**

**At 2 seconds, was Al going up or down?**

*Going down since he was at 6 meters earlier, at 0.6
seconds, going up.*

**When is he at the level of the ski jump again?**

**Al spends a total of 5.2 seconds in the air. How far below
the end of the ski jump does he land?**

**A
basketball player shoots a long shot. The ball has an initial upwards velocity
of 6 meters/seconds. When it is released, it is at the same level of the basket.**

**After
0.3 seconds, how high is the ball above the basket?**

**The
basket is three meters above the gym floor. After 0.3 seconds, how high is the
ball above the gym floor?**

**Assuming
the aim is good, when will the ball go into the basket?**

**The
ball is highest halfway between the time it is thrown and the time it goes into
the basket. **

**-What time is this?**

**-How high is the ball above the gym floor?**

**In an underhand volleyball
serve, the ball leaves the server's hand 1 m above the floor. Suppose that it's
initial upward velocity is 7m/sec. **

**How high above the floor will
it be after 0.3 seconds?**

**If nobody else touches it, when
will it be back to the level where it was served?**

**If nobody else touches it, when
will it be down on the floor?**

**The ball reaches the highest
level halfway between the time it is served and the time it is back at the same
level.**

**-What time is this?**

**-How high above the floor then?**

**A golf ball is hit high into
the air with an initial up-ward velocity of 33 m/sec.**

**How high is it after 3 seconds?**

**When will it be 29 meters above
the ground?**

**Substitute 60 for d and try to
solve for t. What does this tell you about when the ball will be 60 m up?**

**Big guns on naval ships must fire
projectiles many kilometers. To do this, the projectile must go high into the
air. Suppose that the initial upward velocity of a projectile is 300 m/sec.**

**How high will the projectile be 20
seconds after it is fired?**

**When will it reach 1 kilometer above
where it was fired?**

**Will it ever be 5,000 meters above where
it was fired?**

**How long does it take to reach the
target, which is at the same level as the projectile was fired?**

**15. Moon Jumping
Problem**

**
An astronaut on the earth practices jumping to the ground from a spaceship
resting three meters above the ground. The initial upward velocity of the jump
is 4 m/sec.**

**When will the astronaut be back at the
same level as the jump?**

**At what time is the highest point
reached?**

**How high above the ground is that?**

**When does the astronaut reach the
ground?**

**When the astronaut is on the moon, the
gravity is much weaker.**

**The equation there is: **

**
Suppose the initial velocity of the jump is still 4 m/sec.**

**When will the astronaut be at the same
level as the jump?**

**How high above the moon's surface does
the astronaut go?**

**When does the astronaut land on the
moon's surface?**

**16. Sports on the Moon
Problem**

**Since
gravity is much weaker on the moon, an **

**object
thrown upward from its surface reaches an altitude d given by
**

**
**

**Find
the time it takes for each of the following to return to the level from which
they started.
**

**A
high jumper, r = 7 m/seconds.**

**
**

**A
baseball, r = 30 m/seconds.**

**A
golf ball, r = 33 m/seconds.**

**An
arrow, r = 50 m/seconds.**

**Each
of the above will be at its maximum altitude halfway between the time it starts
and the time it gets back down. Find the maximum altitude for each object above.**

**A
high jumper, r = 7 m/seconds.**

**A
baseball, r = 30 m/seconds.**

**A
golf ball, r = 33 m/sec.**

**An
arrow, r = 50 m/seconds.**

**17. Rhoda's Motorcycle
Problem**

**
**

**in
which 5 is replaced by the more precise value 4.893, which is the value at her
latitude, 20 degrees.**

**If
she takes off with an upward initial velocity of r = 13.7 m/sec.**

**When
will she land on the down ramp?**

**What
is the highest she goes above the ground?**

**If
her time of flight is to be precisely 3.7 seconds?**

**What
must her initial upward velocity be?**

**What
is the highest she goes above the ground?**

**If
her initial upward velocity is r = 11 m/sec, will she ever be 9 meters above the
ground (7 meters above the top of the ramp) ? Justify your answer.**

**Suppose that you spring into
the air from the 3-meter diving board. You hit the water, 3 meters below the
board, at 1.6 seconds from the time you sprang.**

**What was your initial upward
velocity, r ?**

**When do you pass the board on
your board on your way back down?**

**How high above the board did
you go?**

**If you spring from the 1-meter
board with the same initial upward velocity as in the first question above, when will you hit
the water?**

**If another diver steps off the
10 meter platform (initial velocity is r = 0) at the same time as you spring
from the 3-meter board who reaches
the water sooner? How much sooner?**

**That's all folks.**