Gravity and Projectile Motion
Name ____________________
During the 16th century, Galileo Galilei did a series of experiments along with some good sound
reasoning. He concluded that all objects, no matter what their weight, would fall at the same rate if
friction with the air could be eliminated.
Although Galileo had crude timing devices, and could not accurately measure the acceleration of a
free-falling object, he could measure the rate at which spheres rolled down inclined planes.
Mathematically extrapolating to a 90 degree incline, he calculated the free fall acceleration without
really measuring it directly. Although we take this approach to science as routine, in Galileo’s time
it was a leap toward abstract generalization that was truly revolutionary.
The acceleration of a free falling object at sea level on Earth is 9.8 m/s2; to solve problems with it
all you have to do is to use the standard kinematics equations we recently studied.
v = d/t
d = ½(vf + vo) t
a =  v/t
d = vot + ½ at2
vf = vo + at
vf2 - vo2 = 2ad
Note: in some problems you can use “g” as + 9.8 m/s2; in other cases, using “g” as – 9.8 m/s2 is the
correct thing to do. What conditions should exist for each case?
1.
How far will a rock fall in 6 seconds if it is released at rest?
d = vot + ½ at2
2.
A ball is thrown down with an initial velocity of 18 m/s. How far will it fall in the first 4
seconds?
d = vot + ½ at2
3.
A ball is thrown up at 22 m/s. How far above the ground will it be in 2 seconds? 4 seconds?
d = vot + ½ at2
Notice there are two terms working in opposition to each other. The v o term increases steadily while the ½ at2 term gets
increasing larger in a negative direction. Thus the ball rises at first, then falls back.
4.
Freddy the Frog does a nice swan dive from a bridge which is 53 meters above the water.
He streamlines himself to eliminate air resistance; how long will it take him to fall to his
aquatic homeland?
d = vot + ½ at2
5.
How long will it take a needle to fall 2.6 cm?
6.
An inquisitive spelunker comes upon a deep cavern with a vertical drop. It is too dark to see
below, so the spelunker drops a rock into the void. 3.8 seconds later the splash is heard. If
the speed of the returning sound wave is 330 m/s, how deep is the cavern?
7.
Rex Things drops a rock from a 42 meter cliff. How long does it take to hit the ground?
8.
A bolt drops off a bridge. How fast is it traveling 2.6 seconds later?
vf = vo + at
9.
A soccer ball is kicked vertically upward at 22 m/s. How long will it take to reach the peak
of its flight?
vf = vo + at
10.
If Foster Pride throws a jar of Cheeze-Whiz directly up at 8.6 m/s, how long will it take to
hit the ground?
vf = vo + at
or
d = vot + ½ at2
11.
A baseball thrown vertically up is aloft for 4.8 seconds before hitting the ground again.
What was its initial velocity?
vf = vo + at
or
d = vot + ½ at2
12.
Struggling with a fire hose, Jean Zon aims a stream of water vertically upwards at 17.3 m/s.
How long before it will take before the stream is falling down at 8.8 m/s?
13.
A projectile is fired up at 27 m/s. How long will it be in flight if a bird catches it is mid air,
while it is falling down, 25 meters above the ground?
d = vot + ½ at2
14.
A ball on a cliff is thrown down at 12 m/s. If the cliff is 77 m tall, how long will it take to
hit the ground?
15.
Now, a ball is thrown up at 19 m/s from the same 77 m tall cliff. How long will it take to hit
the ground now?
16.
A bridge is a height “h” above the ground.
A) How long will it take a rock to fall if released from rest from the bridge? (assume a =
“g”).
B) How long will it take if the rock is thrown down at a velocity of vo?
C) How long will it take if the rock is thrown up at a velocity of vo?
17.
Rosa Corn throws a banana vertically upwards at 24 m/s. How fast is it traveling at a height
of 19 m above the ground?
vf2 - vo2 = 2ad
18.
A champagne cork pops vertically upwards at 8 m/s. To what maximum height will it rise?
(hint: what is its final velocity at the top of its flight?
19.
The bolt from #8 falls 117 meters. How fast is it traveling when it hits the water?
20.
Arthur Mose watches the splash of the bolt in # 19. He tries for a bigger splash by throwing
another bolt down at a velocity of 27 m/s. How long does it take to hit the water 117 meters
below, and how fast will the bolt be moving when it strikes the water?
21.
How fast will a wrench be falling 7.3 seconds after it is accidentally dropped by a worker on
a skyscraper?
22.
How long would it take a diver to hit the water from a 10 meter diving platform?
23.
Our moon has an acceleration of gravity equal to 1.6 m/s2. If an astronaut dropped a moon
rock from a height of 37 meters (off a cliff), how long would it take to hit the ground?
24.
Noel Ivator jumps straight up at 7.2 m/s. How long will he remain in the air?
25.
A cricket ball leaves the bat vertically upward at 35 m/s. On its flight back to Earth it is
eaten by a pelican 57 meters above the ground. How long was the ball in free flight?
26.
To study how meteors form craters, a scientist models the process by dropping ball bearings
into fine granular sand. To get an impact velocity of 8.0 m/s, from what height should she
release the bearings?
27.
Bill Melater, Physics student, drops his calculator off the top of his desk (89 cm high). With
what velocity does it strike the ground?
28.
Eva Destruction spots a potted plant drop by her apartment window at 9 m/s. Further down
the same building, Caesar Boyfriend clocks the pot as going at 27 m/s. How far are Eva and
Caesar apart?
29.
In the gymnasium shower, a leaky shower head drips a drop every 0.3 seconds. The shower
head is 1.9 meters above the ground. When one drop hits the ground, how high off the
ground is the next consecutive drop?