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(solution) 2. Find the components of vtot along the x and y axes in Figure


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2.

 

Find the components of vtot along the x and y axes in Figure 3.25, where ? = 22.5° and vtot = 6.76 m/s.

 

vtot, x =

 

m/s

 

vtot, y =

 

m/s Figure 3.25. 3.

 

You drive 7.50 km in a straight line in a direction 25° East of North.

 

(a) Find the distances you would have to drive straight East and then straight North to

 

arrive at the same point. (This is equivalent to finding the components of the displacement

 

along the East and North directions.)

 

km East

 

km North

 

(b) Show that you still arrive at the same point if the East and North legs are reversed in

 

order. 4.

 

In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal

 

during the day, and he is blown along the following straight lines:

 

2.5 km 45° north of west; then

 

4.70 km 60° south of east; then

 

5.1 km straight east; then

 

7.2 km 55° south of west; and finally

 

2.8 km 5° north of east.

 

What is his final position relative to the island?

 

km

 

° south of east 5.

 

An archer shoots an arrow at a 74.0 m distant target, the bull's-eye of which is at same height as the

 

release height of the arrow.

 

(a) At what angle must the arrow be released to hit the bull's-eye if its initial speed is 37.0

 

m/s? (Although neglected here, the atmosphere provides significant lift to real arrows.)

 

°

 

(b) There is a large tree halfway between the archer and the target with an overhanging

 

branch 3.50 m above the release height of the arrow. Will the arrow go over or under the

 

branch? 6.

 

The cannon on a battleship can fire a shell a maximum distance of 34.0 km.

 

(a) Calculate the initial velocity of the shell.

 

m/s

 

(b) What maximum height does it reach? (At its highest, the shell is above a substantial part

 

of the atmosphere--but air resistance is not really negligible as assumed to make this

 

problem easier.)

 

m

 

(c) The ocean is not flat, since the earth is curved. How many meters lower will its surface

 

be 34.0 km from the ship along a horizontal line parallel to the surface at the ship?

 

m Does your answer imply that error introduced by the assumption of a flat earth in

 

projectile motion is significant here? (Select all that apply.)

 

The error could be significant compared to the size of a target. The error is significant

 

compared to the distance of travel. The error is insignificant compared to the distance of

 

travel. The error is insignificant compared to the size of a target. 7.

 

An owl is carrying a mouse to the chicks in its nest. It is 4.00 m west and 12.0 m above the center of

 

the 30 cm diameter nest and is flying east at 3.50 m/s at an angle 29° below the horizontal when it

 

accidentally drops the mouse. Will it fall into the nest? Find out by solving for the horizontal position

 

of the mouse (measured from the point of release) when it has fallen the 12.0 m.

 

m (from the point of release) 8.

 

A seagull flies at a velocity of 9.00 m/s straight into the wind.

 

(a) If it takes the bird 17.0 min to travel 6.00 km relative to the earth, what is the velocity of

 

the wind?

 

m/s

 

(b) If the bird turns around and flies with the wind, how long will he take to return 6.00

 

km?

 

s

 

(c) Discuss how the wind affects the total round-trip time compared to what it would be

 

with no wind. 9.

 

Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front

 

runner has a velocity of 3.45 m/s, and the second a velocity of 4.20 m/s.

 

(a) What is the velocity of the second runner relative to the first?

 

m/s faster than the front runner.

 

(b) If the front runner is 250 m from the finish line, who will win the race, assuming they

 

run at constant velocity?

 

The first runner will win. The second runner will win.

 

(c) What distance ahead will the winner be when she crosses the finish line?

 

m 10.

 

A ship sets sail from Rotterdam, The Netherlands, heading due north at 7.00 m/s relative to the water.

 

The local ocean current is 1.54 m/s in a direction 40° north of east. What is the velocity of the ship

 

relative to the earth?

 

m/s ° N of E 11.

 

A knife is dropped from the top of a 13.0 m high mast on a ship moving at 1.73 m/s due south.

 

(a) Calculate the velocity of the knife relative to the ship when it hits the deck of the ship.

 

m/s (down)

 

(b) Calculate the velocity of the knife relative to a stationary observer on shore.

 

m/s ° (below the horizontal to the south)

 

(c) Discuss how the answers give a consistent result for the position at which the knife hits

 

the deck. 12.

 

The diagrams below show different objects of equal masses that are acted on by one or more forces. In

 

the diagrams below, each force vector labeled

 

F

 

has the same magnitude. (a) Which of the four objects shown has a net zero force acting on it?

 

(i) (ii) (iii) (iv)

 

(b) Which object or objects have the largest magnitude of force? (Select all that apply.)

 

(i) (ii) (iii) (iv)

 

(c) Which object or objects move with constant velocity? (Select all that apply.)

 

(i) (ii) (iii) (iv)

 

(d) Which object or objects move with changing speed? (Select all that apply.)

 

(i) (ii) (iii) (iv) 13.

 

Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon.

 

The first child exerts a force of 75.0 N, the second a force of 95.0 N, friction is 12.0 N, and the mass of

 

the third child plus wagon is 24.0 kg.

 

(a) What is the system of interest if the acceleration of the child in the wagon is to be

 

calculated? (Select all that apply.)

 

the child in the wagon the children outside the wagon the wagon

 

(b) Draw a free body diagram, including the weight and all other forces acting on the system. (Do this on paper. Your instructor may ask you to turn in this diagram.)

 

(c) Calculate the acceleration.

 

m/s2

 

(d) What would the acceleration be if friction is 20.0 N? 14.

 

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,400 kg.

 

The thrust of its engines is 33,500 N. (Assume that the gravitational acceleration on the Moon is 1.67

 

m/s2.)

 

(a) Calculate its magnitude of acceleration in a vertical takeoff from the Moon.

 

m/s2

 

(b) Could it lift off from Earth? If not, why not?

 

Yes, the thrust of the module's engines is greater than its weight on Earth. Yes, the thrust of the

 

module's engines is equal to its weight on Earth. No, the thrust of the module's engines is equal to its

 

weight on Earth. No, the thrust of the module's engines is less than its weight on Earth.

 

If it could, calculate the magnitude of its acceleration. (If not, enter NONE.)

 

m/s2

 

15.

 

What net external force is exerted on a 1300-kg artillery shell fired from a battleship if the shell is

 

accelerated at 3.00 ? 104 m/s2? (Enter the magnitude.)

 

N

 

What is the magnitude of the force exerted on the ship by the artillery shell?

 

N

 

16.

 

(a) Calculate the tension in a vertical strand of spiderweb if a spider of mass 5.00 ? 10-5 kg hangs

 

motionless on it.

 

N

 

(b) Calculate the tension in a horizontal strand of spiderweb if the same spider sits motionless in the

 

middle of it much like the tightrope walker in Figure 4.13. The strand sags at an angle of 15.0° below

 

the horizontal.

 

N

 

Compare this with the tension in the vertical strand (find their ratio).

 

(tension in horizontal strand / tension in vertical strand) Figure 4.13 17.

 

Consider the baby being weighed in Figure 4.25. Figure 4.25

 

(a) What is the mass of the child and basket if a scale reading of 103 N is observed?

 

kg

 

(b) What is the tension T in the cord attaching the child to the scale?

 

N

 

(c) What is the tension T' in the cord attaching the scale to the ceiling, if the scale has a

 

mass of 0.500 kg?

 

N

 

(d) Draw a sketch of the situation indicating the system of interest used to solve each part.

 

The masses of the cords are negligible. (Do this on paper. Your instructor may ask you to

 

turn in this work.)

 


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