PHY 111 Midterm Questions With Complete Solutions
You could solve this graphically, but you will use algebra for
this example.
Solve for all the velocity vector components. The first vector is
the plane's initial velocity vector.
cos angle = adjacent / hypotenuse
cos 25 = vx / (246 m/s)
vx = 223 m/s
The plane is traveling 223 m/s to the east.
sin angle = opposite / hypotenuse
sin 25 = vy / (246 m/s)
vy = 104 m/s
The plane is traveling 104 m/s to the north.
Plane velocity = <223, 104> m/s
The second vector is the velocity from the wind:
Velocity due to wind = <0, 40 m/s>
The final plane speed is the vector sum of these two velocities:
Σvx = (223 m/s) + (0 m/s) = 223 m/s
Σvy = (104 m/s) + (40 m/s) = 144 m/s
,Final airplane velocity = <223, 144> m/s
Solve for the final velocity magnitude using Pythagorean
theorem and the direction using trig:
a2 + b2 = c2
(223 m/s)2 + (133 m/s)2 = v2
v = 260 m/s
Tanθ = (144 m/s) / (223 m/s)
θ = 33°
The plane's velocity with the tailwind is 260 m/s at 33°
`Equation for volume Correct Answers Volume = length x
width x height
a = Correct Answers = Δv / Δta
= (final velocity - initial velocity) / change in time
A 5.0 kg box accelerates down a 20° ramp with negligible
friction. What is the acceleration of the box? Correct Answers
W = mg = (5 kg)(9.8 N/kg) = 49 N
W┴ = (49 N)(cos 20) = 46 N
W// = (49 N)(sin 20) = 16.8 N
For this problem you only need to consider the forces parallel to
the ramp (the direction the box accelerates).
ΣF// = ma
W// = ma
(16.8 N) = (5.0 kg)(a)
, a = 3.36 m/s/s at -30° (along the surface of the ramp)
A box has a mass of 15 kg. What is the weight of the box?
Report the answer in both newtons and pounds. Correct
Answers W = mg
W = (15 kg)(9.8 N/kg)
W = 147 N
There are 4.4 N = 1lb
(147 N)(1 lb / 4.4 N) = 33.4 lb
A car moves forwards at a speed of 20 m/s for 5 seconds. What
is the distance the car has traveled? What is its displacement?
Correct Answers x = vt + xox - xo = (20 m/s)(5 s)Δx = 100 m
forwards
A car moving at a speed of 10 m/s slows to a stop over a
distance of 30 m. What was the acceleration of the car? Correct
Answers v2 = 2aΔx + vo2
0 = 2(a)(30 m) + (10 m/s)^2
a = -1.7 m/s2
A car moving at a speed of 20 m/s slows to a stop over 5
seconds. What is the acceleration of the car? Correct Answers
v = at + vo
0 = (a)(5 s) + (20 m/s)
a = -4 m/s/s
A car traveling at a speed of 20 m/s slows at a rate of 5 m/s/s for
2 seconds. How far did the car travel while stopping? Correct
Answers x = 1/2at2 + vot + xo
You could solve this graphically, but you will use algebra for
this example.
Solve for all the velocity vector components. The first vector is
the plane's initial velocity vector.
cos angle = adjacent / hypotenuse
cos 25 = vx / (246 m/s)
vx = 223 m/s
The plane is traveling 223 m/s to the east.
sin angle = opposite / hypotenuse
sin 25 = vy / (246 m/s)
vy = 104 m/s
The plane is traveling 104 m/s to the north.
Plane velocity = <223, 104> m/s
The second vector is the velocity from the wind:
Velocity due to wind = <0, 40 m/s>
The final plane speed is the vector sum of these two velocities:
Σvx = (223 m/s) + (0 m/s) = 223 m/s
Σvy = (104 m/s) + (40 m/s) = 144 m/s
,Final airplane velocity = <223, 144> m/s
Solve for the final velocity magnitude using Pythagorean
theorem and the direction using trig:
a2 + b2 = c2
(223 m/s)2 + (133 m/s)2 = v2
v = 260 m/s
Tanθ = (144 m/s) / (223 m/s)
θ = 33°
The plane's velocity with the tailwind is 260 m/s at 33°
`Equation for volume Correct Answers Volume = length x
width x height
a = Correct Answers = Δv / Δta
= (final velocity - initial velocity) / change in time
A 5.0 kg box accelerates down a 20° ramp with negligible
friction. What is the acceleration of the box? Correct Answers
W = mg = (5 kg)(9.8 N/kg) = 49 N
W┴ = (49 N)(cos 20) = 46 N
W// = (49 N)(sin 20) = 16.8 N
For this problem you only need to consider the forces parallel to
the ramp (the direction the box accelerates).
ΣF// = ma
W// = ma
(16.8 N) = (5.0 kg)(a)
, a = 3.36 m/s/s at -30° (along the surface of the ramp)
A box has a mass of 15 kg. What is the weight of the box?
Report the answer in both newtons and pounds. Correct
Answers W = mg
W = (15 kg)(9.8 N/kg)
W = 147 N
There are 4.4 N = 1lb
(147 N)(1 lb / 4.4 N) = 33.4 lb
A car moves forwards at a speed of 20 m/s for 5 seconds. What
is the distance the car has traveled? What is its displacement?
Correct Answers x = vt + xox - xo = (20 m/s)(5 s)Δx = 100 m
forwards
A car moving at a speed of 10 m/s slows to a stop over a
distance of 30 m. What was the acceleration of the car? Correct
Answers v2 = 2aΔx + vo2
0 = 2(a)(30 m) + (10 m/s)^2
a = -1.7 m/s2
A car moving at a speed of 20 m/s slows to a stop over 5
seconds. What is the acceleration of the car? Correct Answers
v = at + vo
0 = (a)(5 s) + (20 m/s)
a = -4 m/s/s
A car traveling at a speed of 20 m/s slows at a rate of 5 m/s/s for
2 seconds. How far did the car travel while stopping? Correct
Answers x = 1/2at2 + vot + xo
