PHY 2053 Midterm: Sum12Exam1Solutions
1
PHY2053
Summer 2012
Exam 1 Solutions
1. The period is proportional to the square root of its length
LT ∝
Forming a ratio:
1
2
1
2
L
L
T
T=
We want T
2
= 1.5 T
1
. Substituting
25.2)5.1(
5.1
5.1
2
1
2
1
2
1
2
1
1
==
=
=
L
L
L
L
L
L
T
T
2. second
feet
88
mile1
feet5280
seconds60
minute1
minutes60
hour1
hour
miles
60
hour
miles
60 =×××=
3. The definition of average velocity is
t
x
v
avx
∆
∆
=
,
where
∆
x
is the total distance traveled. For the first part of the trip,
miles5.52hour
4
3
hour
miles
70
11
=×=∆=∆
tvx .
For the second part,
miles25hour
2
1
hour
miles
50
22
=×=∆=∆
tvx
Overall,
2
miles/hour62
hour5.0hour75.0
miles25miles5.52
,
=
+
+
=
∆
∆
=
t
x
v
avx
4. Use
2
22
22
22
m/s6.3
)m20(2
)m/s9()m/s15(
2
2
=
−
=
∆
−
=
∆=−
x
vv
a
xavv
ixfx
ixfx
5. First find the time it takes for the cage to hit the ground.
s26.2
m/s8.9
)m25(22
)(0
)(
2
2
2
1
2
2
1
=
−−
=
∆−
=∆
∆−=
∆+∆=∆
g
y
t
tg
tatvy
yiy
Princess needs to run 3 m in that time.
2
22
2
2
1
2
2
1
m/s18.1
)s26.2(
)m3(2
)(
2
)(0
)(
==
∆
∆
=
∆+=
∆+∆=∆
t
x
a
ta
tatvx
x
x
xix
6. Solve for the initial speed.
m/s13.8
2
)s7.3)(m/s8.9(
s7.3
m37
2
)(
)(
2
2
2
1
2
2
1
=+
−
=
∆
+
∆
∆
=
∆−∆=
∆+∆=∆
tg
t
y
v
tgtv
tatvy
iy
iy
yiy
7. Find the components of each vector. For the tee shot
yards13030cosyards)150(30cos
yards7530sinyards)150(30sin
===
===
AA
AA
y
x
For the second shot
3
C
B
A
yards9.8445cosyards)120(45cos
yards9.8445sinyards)120(45sin
===
−=−=−=
BB
BB
y
x
Add like components
yards215)yards9.84(yards)130(
yards9.9)yards9.84(yards)75(
=+=+=
−
=
−
+
=
+
=
yyy
xxx
BAC
BAC
The calculator gives
87
9.9
215
tan
1
−=
−
=
−
θ
Since the x-component is negative, we add 180
o
to get 93
o
or 3
o
W of N.
8. We have
0=++ CBA
Taking components
0=++
xxx
CBA 0=++
yyy
CBA
Solve for C
x
and C
y
xxx
BAC −−=
yyy
BAC −−=
We need the components of
A
and
B
:
N3.4330cos)N50(cos ===
Ax
AA
θ
N0.2530sin)N50(sin ===
Ay
AA
θ
Document Summary
The period is proportional to the square root of its length. The definition of average velocity is v avx x t where x is the total distance traveled. For the first part of the trip, tv. First find the time it takes for the cage to hit the ground. y t v iy. Princess needs to run 3 m in that time. x t v ix. Solve for the initial speed. y t v iy v iy t a y t. Since the x-component is negative, we add 180o to get 93o or 3o w of n. We need the components of a (cid:2) and b. But since cx is negative, add 180o to get 245o. The relative velocity equation for this situation is (cid:2) v. The velocity of the ground relative to the car is the negative of the car relative to the ground, and (cid:2) v. If a projectile is shot horizontally, viy = 0.
