Physics 140 – Fall 2014
September 15
Projectile Motion
U.S.S. Missouri firing 16-inch shells - J.D. Rogers
Reminder:
• Mastering Physics homework #1 due tomorrow night at
midnight
1
Starting today with math quiz
Credit equivalent to four i>clicker questions
(points independent of correctness)
Please write your name on quiz booklet and scantron.
Include student ID on scantron. Turn both in.
To earn quiz credit, answer the following
question – who won Saturday’s game?
A) U-M
B) Miami of Ohio
3
Questions concerning
today’s youtube videos?
4
5
Projectile motion
• Two balls begin at rest at the same height (but not at
the same place). At time t = 0, one of them (A) is
simply released, and the other one (B) is launched
straight horizontally. (After t = 0, both of them are
then freely falling.) Which one hits first? Ignore air
resistance.
A.
B.
C.
D.
Let’s find out!
Ball A hits the ground first
Ball B hits the ground first
They both hit the ground simultaneously
The answer depends on which one is heavier
Book problem – part 1 (based on E3.9)
A physics book slides off a horizontal tabletop with a speed of
1.10 m/s. It strikes the floor in 0.350 s. Ignore air resistance.
What is the height H of the tabletop above the floor?
A)
B)
C)
D)
E)
0.300 m
0.600 m
0.900 m
1.20 m
1.50 m
1 2
y  y0  v0 yt  ayt
2
1 2
0  H  0  gt
2
1
 H  gt 2  (0.5)(9.80 m/s 2 )(0.350 s)2  0.600 m
2
H
y
x
x motion
irrelevant!
7
Book problem – part 2 (based on E3.9)
A physics book slides off a horizontal tabletop with a speed of
1.10 m/s. It strikes the floor in 0.350 s. Ignore air resistance.
What is the horizontal distance from the edge of the table to the
point where the book strikes the floor?
A)
B)
C)
D)
E)
0.385 m
0.458 m
0.658 m
0.758 m
0.858 m
1
x  x0  v0 x t  ax t 2
2
D  0  v0 x t  0  (1.10 m/s)(0.350 s) = 0.385 m
H
y
x
y motion
irrelevant!
8
Book problem - part 3 (based on E3.9)
A physics book slides off a horizontal tabletop with a speed of
1.10 m/s. It strikes the floor in 0.350 s. Ignore air resistance.
What is the speed of the book just before it reaches the floor?
A)
B)
C)
D)
E)
1.10 m/s
2.30 m/s
3.60 m/s
5.10 m/s
6.50 m/s
vx  v0 x  ax t  v0 x
vy  v0 y  ayt  gt
H
y
x
v  vx2  vy2  (1.10 m/s)2  [(9.80 m/s 2 )(.350 s)]2  3.60 m/s
9
Forest Fire problem (based on P3.53)
In fighting forest fires, airplanes work in support of ground
crews by dropping water on the fires. A pilot is practicing
by dropping a canister or red dye, hoping to hit a target on
the ground below. If the plane is flying in a horizontal path
90.0 m above the ground and with a speed of 64.0 m/s (143
mi/h), at what horizontal distance from the target should
the pilot release the canister? Ignore air resistance.
A)
B)
C)
D)
E)
166 m
202 m
239 m
274 m
311 m
Guardian 2008
10
v0  (64.0 m/s) iˆ
Drop
point
v
H = 90. m
D
Target
Distance D is
A) 166 m
B) 202 m
C) 239 m
D) 274 m
E) 311 m
11
v0  (64.0 m/s) iˆ
Drop
point
v
H = 90. m
D
Target
Similar to book problem:
1 2
Need drop time t such that H  gt
2
t 
2H

g
2(90.0 m)
 4.28 s
2
9.8 m/s
 D  v0x t  (64.0 m/s)(4.3 s) = 274. m
12
Tilted Rocket problem – part 1 (based on P3.47)
A test rocket is launched by accelerating it along a 200.0-m
incline at 1.25 m/s2 starting from rest at point A on the diagram.
The incline rises at 35.0° above the horizontal, and at the instant
the rocket leaves the incline, its engines turn off and it is subject
only to gravity (ignore air resistance).
What is the maximum height above the ground that the rocket
Reaches?
x0 = (200.0 m) cos(35.0°) = 163.8 m
A) 67 m
y0 = (200.0 m) sin(35.0°) = 114.7 m
2
v0  2as
B) 94 m
v0
C) 123 m  v  2(1.25 m/s2 )(200. m)  22.4 m/s
0
D) 156 m
E) 199 m
(x0, y0)
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At the top:
 H  y0 
vy2  0  v02y  2ay (y  y0 )  v02y  2g(H  y0 )
v02y
2g
 H  y0 
v02y
2g
[(22.4 m/s)(sin(35o)]2
 H  114.7 m +
 123. m
2
(2)(9.8 m/s )
v0
(x0, y0)
H
R
14