SAMPLE EXAM I SOLUTIONS:
1.
2.
3.
PHY 1114
Fall 2012
Professor K. Tapp
Give the fundamental unit in the system specified.
a)
___meter___________ SI unit of length
b)
___foot____________
c)
___second__________ SI unit of time
British unit of length
Give the agreed SI prefix for each power-of-10 multiple.
a)
____mega-__________ 106
b)
____centi-_________
10-2
c)
____kilo-__________
k
Convert 60 mph to km/sec if
1 mile = 1.6 km,
1 hour = 60 min,
1 min = 60 sec
60 mile/hour x 1.6 km/mile = 96 km/hour
1 hour/60 min x 1 min/60 sec = 1 hour/3600 sec
96 km/hour x 1 hour/3600 sec = 0.027 km/sec
4.
Define a vector quantity and a scalar quantity and given an example of each.
A vector has magnitude & direction.
A scalar has only magnitude.
5.
Find the x and y components of this vector.
= 4 N at a direction of 35° with respect to the x axis.
Ax = A cosθ
Ax = (4)(cos35)
Ax = 3.28
6.
Ay = A sinθ
Ay = (4)(sin35)
Ay = 2.29
Find the magnitude and direction of a vector whose components are: Bx = +7 m By = +3 m
tanθ = 3/7 = 0.42857
θ = tan-1(0.42857)
θ = 23.1985°
a2 + b2 = c2
72 + 32 = c2
49 + 9 = 58 = c2  √58 = √c2
c = B = 7.62
1
7.
A runner travelling at a constant speed runs 105 m in 15 s. (a) What is the runner's average speed? (b)
How far will the runner go in 20 s?
8.
A Boeing 727 jet airliner accelerates uniformly from rest to 86 m/s in 40 s.
(a) What is its average acceleration?
(b) If the average were 1.85 m/s2, how fast would it be traveling after 40 s, starting from rest?
9.
An automobile enters a freeway on-ramp with an initial speed of 40 ft/sec and accelerates at 3.0 ft/s2 for
10 seconds. (a)How far does the car travel? (b)What is the final speed of the automobile?
2
10.
A stone is thrown vertically upward with an initial speed of 30 ft/s. Find (a) how high the stone rises,
and (b) the time for the stone to return to the thrower.
g = 9.8 ms-2 = 32.2 fts-2
11.
If the Sun is a distance of 1.5 x 108 km from the Earth, how long, in minutes, does it take sunlight to
reach the Earth if it moves at a constant speed of 3 x 108 m/s?
d = 1.5 x 108 km = 1.5 x 1011 m
V = 3 x 108 m/s
t=?
V=d/t
t =d/V
t = (1.5 x 1011 m) / (3 x 108 m/s)
t = 500 s
t = 8.3 minutes
3
12.
An airplane which has a 420 mi/hr ground speed in still air is flying with its nose toward the north. A 60
mi/hr wind is blowing 30° south of west. What are the magnitude and direction of the airplane's velocity
relative to the ground?
13.
A slingshot is used to project a pebble with an initial velocity of 40 m/s at an angle of 60° above the
horizontal. Find (a) the maximum height, and (b) the range of the pebble.
4
14.
At the instant a ball rolls off a rooftop it has a horizontal velocity component of +10.0 m/s and a vertical
component (downward) of 15.0 m/s. Determine (a) the angle of the roof, and (b) what is the ball’s speed
as it leaves the roof?
tan θ = 15 / 10
θ = tan-1 (15/10)
θ = 56.3°
a2 + b2 = c2
√(102 + 152) = c
√(325) = c
18 m/s = c
15.
16.
A baseball player hits a home run into the right field upper deck. The ball lands in a row that is 135 m
horizontally from home plate and 25.0 m above the playing field. An avid fan measures its time of flight
to be 4.10 s. Determine (a) the ball’s velocity components, and (b) the angle of its initial velocity.
(a)
=
(b)
θ =
135 m
4.10 s
= 32.9 m/s ,
=
25.0 m
4.10 s
= 6.10 m/s
10.5° above horizontal .
A meteorologist tracks the movement of a thunderstorm with Doppler radar. At 8:00 pm, the storm was
60 mi northeast of his station. At 10:00 pm, the storm is at 75 mi north. Determine (a) the average
velocity of the storm, and (b) the general direction of the thunderstorm’s velocity: (2) north of west
Break into components:
1
= (60 mi)[(cos 45°) ^
x + (sin 45°) ^
y] = (42.4 mi) ^
x + (42.4 mi) ^
y
2
= (75 mi) ^
y
2 − 1
= (75 mi) ^
y − [(42.4 mi) ^
x + (42.4 mi) ^
y]
= (−42.4 mi) ^
x + (32.6 mi) ^
y.
Therefore
d = (−42.4 mi)2 + (32.6 mi)2 = 53.48 mi.
53.48mi
Thus v =
= 26.7 mi/h
2.0h
d
d2 = 75
mi
d1 = 60
mi
Station
€
5
17.
An object is observed to fall from a bridge, striking the water below 2.50 s later. (a) With what velocity
did it strike the water? (b) How high is the bridge?
6