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Physics: Velocity, Magnitude and Direction

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Hi, I need some assistance with the following questions:

1. A cannon ball is fired with a velocity of 48 m/s at 42 degrees up from the horizontal. Assume that it lands at the same level as it was fired from.
a. Find the maximum height of the cannon ball.
b. Find the total time the cannon ball is in the air.
c. Find the range of the cannon ball.

2. A rock is thrown off a vertical cliff with a horizontal velocity of 15 m/s. If the rock lands 25 m from the base of the cliff, how tall is the cliff?
(A) 8 m (B) 14 m (C) 16 m (D) 34 m

3. Velocity A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in length and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the vectors(a) A + B and (b) A - B.

4. A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 degrees above the horizontal. Next, it travels 135 ft at an angle of 40 degrees below the horizontal. Use graphical techniques to find the roller coaster's displacement from its starting point to the end of this movement.

5. A jogger runs 100 m due west, then changes direction for the second leg of the run. At the end of the run, she is 175 miles away from the starting point at an angle of 15.0 degrees north of west. What were the direction and length of her second displacement? Use graphical techniques.

6. The magnitude of vector A is 35.0 units and points in the direction 325 degrees counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.

7. A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

8. A brick is thrown upward from the top of a building at angle of 25 degrees to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building?

9. A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0 degrees above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile's velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?

10. A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.0 m/s aimed directly north relative to the water.
(a) What is the velocity of the boat relative to the shore.
(b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north

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Physics: velocity, speed, force, temperature, energy, magnitude, acceleration, wave

1) A particle moves according to the equation x=10t2, where x is in meters and t is in seconds. Find the average velocity for the time interval from 2.0 second to 2.1 second.
A) 41 m/s
B) 100 m/s

2) If A = (12i -16j) and B = (-24i + 10j), what is the magnitude of the vector C = (2A - B)?
A) 42
B) 22
C) 64
D) 90

3) A room measures 3.0 m by 4.5 m by 6.0 m. The heating and air conditioning ducts to and from the room are circular with diameter 0.30 m, and the air in the room is to be exchanged every 12 minutes. What is the necessary flow speed in the duct? (Assume that the density of the air is constant)
A) 0.6 m/s
B) 1.6 m/s
C) 3.2 m/s
D) 4.1 m/s

5) A 50-kg ice skater is moving at 5 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 1 m around the pole. Determine the force exerted by the rope on her arms.
A) 1250 N
B) 250 N
C) 50 N
D) 1100 N

6) Steam at 1000C is added to ice at O0C. The mass of the steam is 10.0 g and the mass of the ice is 50.0 g. What is the final temperature of the mixture?
A) 20.4oC
B) 40.4oC
C) 80.8oC
D) 90.1oC

7) The speed of a 4.0-kg object is given by v = (2t) m/s, where t is in seconds. At what rate is the resultant force on this object doing work at t = 1 second?
A) 48 W
B) 40 W
C) 56 W
D) 16 W

8) A 10-kg object is initially at the top of a rise, at point A. It then moves down to point B. Choose point B to be the zero level for gravitational potential energy. Find the change in potential energy of the object if point B is 10 m lower than point A.
A) - 980
B) - 10
C) - 100
D) - 98

9) A 3-kg particle has a velocity of (3i - 4j) m/s. Find the magnitude of its momentum.
A) 9 kg.m/s
B) -12 kg.m/s
C) 15 kg.m/s
D) 3 kg.m/s

10) At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2 rad/s. Two seconds later it has turned 5 complete revolutions. What is the angular acceleration of this wheel?
A) 17 rad/s^2
B) 14 rad/s^2
C) 20 rad/s^2
D) 23 rad/s^2

11) A car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg.m^2/s) relative to the center of the racetrack?
A) 5 x 10^2
B) 5 x 10^6
C) 2.5 x 10^6
D) 2.5 x 10^4

14) How many significant figures are in the following number? 0.0064
A) 2
B) 3
C) 4
D) 5

15) In order to understand the concept of temperature it is useful to understand
A) the zeroth law of thermodynamics
B) the first law of thermodynamics
C) the second law of thermodynamics
D) none of the above

16) An archer shoots an arrow with a velocity of 45 m/s at an angle of 50 degrees with the horizontal. What is the height of the arrow at a point 150 meters downrange?
A) 4.7 m
B) 47.0 m
C) 5.6 m
D) 56.0 m

17) A sinusoidal wave is described by y=(0.30 m)sin(0.20x-40t ). Determine the wave speed.
A) 100 m/s
B) 133 m/s
C) 150 m/s
D) 200 m/s

18) The exhaust temperature of a Carnot heat engine is 350oC. What is the intake temperature if the efficiency is 25.0%?
A) 400oC
B) 543oC.
C) 558oC
D) 830oC

20) A house has well-insulated walls. It contains a volume of 100 m3 of air at 300 K. Calculate the energy required to increase the temperature of this diatomic gas by 2oC. Assume it is heating at constant pressure and use Cp=7R/2.
A) 118 kJ
B) 236 kJ
C) 354 kJ
D) 472 K

21) If the speed at some point in a fluid changes with time, the fluid flow is not __________.
A) steady
B) irrotational
C) incompressible
D) nonviscous

22) A bowling ball rolls without slipping on a flat surface. The ball has ___________.
A) rotational kinetic energy
B) translational kinetic energy
C) both a and b
D) neither a or b

23) In uniform circular motion, there is a ____________.
A) constant velocity
B) constant angular velocity
C) zero acceleration
D) net tangential acceleration

24) Linear momentum is ____________.
A) always conserved
B) a scalar quantity
C) a vector quantity
D) unrelated to force

25) If the net force on an object is zero, the object must _______________.
A) be at rest
B) be in motion with constant velocity
C) have zero acceleration
D) none of these

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