PHYS 2211 Module 2 Self Assessment Practice Problems

Module 2 Self Assessment Practice Problems

2.1
The magnitudes of two displacement vectors are A = 20 m and B = 6 m. What are the largest and the smallest values of the magnitude of the resultant ?
Answer: 26 m, 14 m (Click and drag over the answer to highlight it)
2.2
You drive 7.50 km in a straight line in a direction 15° east of north.
(a) Find the distances you would have to drive straight east and then straight north to arrive at the same point.
(b) Show that you still arrive at the same point if the east and north legs are reversed in order. Assume the +x-axis is to the east.
Answer: 1.94 km, 7.24 km
2.3
A particle undergoes three consecutive displacements given by vectors , , and .
(a) Find the resultant displacement vector of the particle.
(b) What is the magnitude of the resultant displacement?
(c) If all displacements were along one line, how far would the particle travel?
Answer: (a) , (b) R = 8.18 mm, (c) 2.163 cm
2.4
A small plane flies 40.0 km in a direction 60° north of east and then flies 30.0 km in a direction 15° north of east.
(a) Find the total distance the plane covers from the starting point.
(b) Find the geographic direction of its displacement vector.
(c) What is its displacement vector? Express it in vector notation.
Answer: (a) 70 km, (b) 40.9° north of east, (c) where is to the east.
2.5
A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. Assume the +x-axis is to the east.
(a) Find his net displacement vector.
(b) How far is the restaurant from the post office?
(c) If he returns directly from the restaurant to the post office, what is his displacement vector on the return trip?
(d) What is his compass heading on the return trip?
Answer: (a) , (b) R = 134.32 km, (c) , (d) 80.2° south of west
2.6
An adventurous dog strays from home, runs three blocks east, two blocks north, and one block east, one block north, and two blocks west. Assuming that each block is about 100 yd, find the dog’s net displacement vector, its magnitude, and its direction. Assume the +x-axis is to the east.
Answer : , D = 360.5 yd, 56.3° north of east
2.7

A barge is pulled by the two tugboats shown in the figure. One tugboat pulls on the barge with a force of magnitude 4000 units of force at 15° above the line AB (see the figure) and the other tugboat pulls on the barge with a force of magnitude 5000 units of force at 12° below the line AB. Resolve the pulling forces to their x- and y-components and find the components of the resultant force pulling on the barge.
(a) What is the magnitude of the resultant pull?
(b) What is its direction relative to the line AB?
Answer: 8754 units of force, approximately along AB
2.8
Find the angles that vector makes with the x-, y-, and z-axes.
Answer: 64.12°, 150.79°, 77.39°
2.9
A stubborn dog is being walked on a leash by its owner. At one point, the dog encounters an interesting scent at some spot on the ground and wants to explore it in detail, but the owner gets impatient and pulls on the leash with force along the leash.
(a) What is the magnitude of the pulling force?
(b) What angle does the leash make with the vertical? (Assume the vertical is along the z-axis.)
Answer: (a) 167.5 N, (b) 79°
2.10
If the velocity vector of a polar bear is , how fast and in what geographic direction is it heading? Here, and are directions to geographic east and north, respectively.
Answer: 22.2 km/h, 35.8° South of West