Download Test #4 - Wando High School

Applying Vectors to Real-Life Situations
Name_____________________________
FOLLOW THESE DIRECTIONS:
Be sure every vector has an arrowhead! Show all of your work. Give a cal. And a rounded answer for each final
answer. Circle intermediate answers. Show and box all formulas you use. Then show a set up with numbers and units
inserted in the formula. Did you read these directions? YES (circle yes)
Basic 2 vector
1.
A helicopter is traveling at 0 degrees/east at 350.0 km/hr. But a 80.54 km/hr wind is blowing 270
degrees southward.
a) What are the direction and magnitude of the resultant vector?
b) How far will the helicopter travel eastward in 2.50 hrs?
c) A swimmer is moving 2.5 m/s westward as a current flowing 1.2 m/s pushes him northward. What is
the magnitude and direction of the swimmer?
Component vectors
d) What are the two components of a vector that represents a car moving at 44.4 m/s at 112 o?
e) What is the upward (northward) component vector of a cannon ball launched at 80.0 m/s @ 65.00?
Rope Pulling problems
2) The “Lawn Ranger” pushes a 117.6 Newton mower with an applied force of 84.5 N at an angle
48.00 to the ground. What will the magnitude of the acceleration of the mower be in this situation?
(assume no friction)
3) A 24N crate is pulled by a rope with 30.0 N at a 36.00 ground. The coefficient of friction force in this
scenario is .222. At what rate will the crate accelerate? (hint: the normal force will not be 24 N- why not?)
4) A child pulls an 8.00 kg sled with a rope at a 38.00 ground angle resulting in an acceleration of 4.70 m/s2.
If this is frictionless, with how much force must the child be pulling?
Hanging Object Problems
5) The sign’s weight is 336 N. Note the angles given. Find the tensional force on all three support rods. The
middle rod is perfectly vertical.
rod A
38.80
rod B
rod C
71.40
6) A sign is hung using two ropes attached to the top center of the sign. The angle between the ropes is
24.00. If there is 34 Newtons of tensional force on each rope, what is the mass of the sign?
Incline Plane Problems
7) A 5.5 kg suitcase rests on a 22.00 slope.
a) What is the force of friction?
b) What is the coefficient of friction?
8) An 8.55kg box slides down a 46.0 0 incline.
a) If the incline is frictionless, what is the acceleration of the box?
b) If the incline has a coefficient of friction of .550, what is the acceleration in reality?
**9) A 45.0 kg block is on an inclined plane of 27.4 o. It is connected by a rope through a pulley, to a 30.0
kg block that is hanging off the other side. Calculate the distance that the 30.0 kg block will move in 2.00
sec starting from rest. (find out if it goes up or down first!) (Neglect friction)
10) A child pulls a rope attached to a sled up a 25.0 degree incline (the rope is pulled parallel to the
surface of the incline). The mass of the sled is 8.00 Kg. The child uses a constant force of 78.4N. As the
sled is pulled along the incline, what is the acceleration of the sled? Assume frictionless
**11) Two 60.5 kg boxes are connected by a cord passing over a pulley. Box A is on a horizontal surface,
box B is on a 35.0o incline sloping westward (down and to the left). If the coefficient of friction is .15
for both, find the acceleration of the box B- include a magnitude and a direction.
River Problem
12) A boat traveling due east at 6.00 m/s crosses a 98.0 m wide river flowing due southward at 3.40 m/s.
a) What will the boat’s velocity be? (remember that velocity, like all vectors, has both a magnitude
and direction).
b) How far downstream will the boat be when it reaches the opposite shore?
c) How long will it take the boat to reach the opposite shore of the river?
13) A helicopter is caught in a strong wind current. It tries to fly due west at 25.5 m/s. The wind is
currently blowing due north at 12.0 m/s. By the time it travels 150.0 m due west using its engines power,
how far will it have flown due north due to the air current?
Non-900 problems
14) Two forces act on an object. One is 78 N and acts at 60.0 0. The other is a 53.8 N force at 2700. What is
the equilibrant force that would exactly counteract these two forces?
15) A cord attached to an armadillo is pulled with 8.00N of force at 0.00 0. Another chord attached to the
same critter is pulled with 12.0 N and is pulled at 298 0. What will the overall direction and magnitude of
the force in this armadillo.
Student provided answers
1)a. 359.1, 347.040 b. 875 km C)2.8 m/s @ 1540
D) 17 m/s W, 41 N E) 72.5 m/s North 2) 4.71 ms2
2
3) 9.6 m/s 4) 47.7 N 5) a) 179N cable b) 112N cable c. 118N 6) 6.7 kg
7) a. 20. N b. .40 ( did
you get.37? don’t use the force of weight in the friction formula! Use the force NORMAL (perpendicular)
8) a. 7.05 m/s2 b. 3.31 m/s2 9)2.4m 10) 5.66 m/s2
11) 1?.47 m/s2 12) a. 6.90m/s, 330.50 b. 55.4 m
c.16.3 sec 13) 70.6 north 14) 41 N @ 200.0
15) 17.3N, 3220