Paul Peter Urone; Roger Hinrichs

Problems

5.1 Vector Addition and Subtraction: Graphical Methods

25 .

A person attempts to cross a river in a straight line by navigating a boat at

15\,\text{m/s}

. If the river flows at

5.0\,\text{m/s}

from his left to right, what would be the magnitude of the boat’s resultant velocity? In what direction would the boat go, relative to the straight line across it?

The resultant velocity of the boat will be $10.0\,\text{m/s}$ . The boat will go toward his right at an angle of $26.6^\circ\!$ to a line drawn across the river.
The resultant velocity of the boat will be $10.0\,\text{m/s}$ . The boat will go toward his left at an angle of $26.6^\circ\!$ to a line drawn across the river.
The resultant velocity of the boat will be $15.8\,\text{m/s}$ . The boat will go toward his right at an angle of $18.4^\circ\!$ to a line drawn across the river.
The resultant velocity of the boat will be $15.8\,\text{m/s}$ . The boat will go toward his left at an angle of $18.4^\circ\!$ to a line drawn across the river.

26 .

A river flows in a direction from southwest to northeast at a velocity of

7.1\,\text{m/s}

. A boat captain wants to cross this river to reach a point on the opposite shore due east of the boat’s current position. The boat moves at

13\,\text{m/s}

relative to the water. Which direction, relative to the water, should the boat head toward? Note that the resultant direction (relative to the shore) is 0°.

It should head in a direction $22.6^\circ\!$ east of south.
It should head in a direction $22.6^\circ\!$ south of east.
It should head in a direction $45.0^\circ\!$ east of south.
It should head in a direction $45.0^\circ$ south of east.

5.2 Vector Addition and Subtraction: Analytical Methods

27.

A person walks 10.0 m north and then 2.00 m east. Solving analytically, what is the resultant displacement of the person?

$\vec{R}$ = 10.2 m, θ = 78.7º east of north
$\vec{R}$ = 10.2 m, θ = 78.7º north of east
$\vec{R}$ = 12.0 m, θ = 78.7º east of north
$\vec{R}$ = 12.0 m, θ = 78.7º north of east

28 .

A person walks

12.0^\circ\!

north of west for

55.0\,\text{m}

and

63.0^\circ\!

south of west for

25.0\,\text{m}

. What is the magnitude of his displacement? Solve analytically.

$10.84\,\text{m}$
$65.1\,\text{m}$
$66.04\,\text{m}$
$80.00\,\text{m}$

5.3 Projectile Motion

29 .

A water balloon cannon is fired at

30\,\text{m/s}

at an angle of

50^\circ\!

above the horizontal. How far away will it fall?

$2.35\,\text{m}$
$3.01\,\text{m}$
$70.35\,\text{m}$
$90.44\,\text{m}$

30.

A person wants to fire a water balloon cannon such that it hits a target 100 m away. If the cannon can only be launched at 45° above the horizontal, what should be the initial speed at which it is launched?

31.3 m/s
37.2 m/s
980.0 m/s
1,385.9 m/s

5.4 Inclined Planes

31 .

A coin is sliding down an inclined plane at constant velocity. If the angle of the plane is

10^\circ\!

to the horizontal, what is the coefficient of kinetic friction?

$\mu_\text{k} = 0$
$\mu_\text{k} = 0.18$
$\mu_\text{k} = 5.88$
$\mu_\text{k} = \infty$

32.

A skier with a mass of 55 kg is skiing down a snowy slope that has an incline of 30°. Find the coefficient of kinetic friction for the skier if friction is known to be 25 N .

$μ k = 0$
$μ k = 0.05$
$μ k = 0.09$
$μ k = ∞$

5.5 Simple Harmonic Motion

33 .

What is the time period of a

6\,\text{cm}

long pendulum on earth?

$0.08\,\text{s}$
$0.49\,\text{s}$
$4.9\,\text{s}$
$80\,\text{s}$

34 .

A simple harmonic oscillator has time period

4\,\text{s}

. If the mass of the system is

2\,\text{kg}

, what is the force constant of the spring used?

$0.125\,\text{N/m}$
$0.202\,\text{N/m}$
$0.81\,\text{N/m}$
$4.93\,\text{N/m}$