1. After an airplane takes off, it
travels 10.4 km west, 8.7 km north, and 2.1 km up. How far

is it from the takeoff
point?

2. Two ropes in a vertical plane exert
equal-magnitude forces on a hanging weight but pull with an angle of 86.0° between them. What pull does each one exert if their resultant
pull is 372 N directly upward?

3. You are hungry and decide to go to
your favorite neighborhood fast-food restaurant. You leave your apartment and
take the elevator 10 flights down (each flight is 3.0 m) and then go 15 m south
to the apartment exit. You then proceed 0.2 km east, turn north, and go 0.1 km
to the entrance of the restaurant. (a) Determine the displacement from your apartment
to the restaurant. Useunit vector notation for your answer, being sure to make
clear yourchoice of coordinates. (b) How far did you travel along the path you
took from your apartment to the restaurant, and what is the magnitude of the
displacement you calculated in part (a)?

4. While following a treasure map, you
start at an old oak tree. You first walk 825 m directly south, then turn and
walk 1.25 km at 30.0° west of north, and finally walk 1.00 km at 40.0° north of
east, where you find the treasure: a biography of Isaac Newton! (a) To return
to the old oak tree, in what direction should you head and how far will you
walk? Use components to solve this problem. (b) To see whether your calculation
in part (a) is reasonable, check it with a graphical solution drawn roughly to
scale.

5. A ship leaves the island of Guam
and sails 285 km at 40.0° north of west. In which direction must it now head and how far must it sail so that its resultant
displacement will be 115 km directly east of Guam?

6. A one-euro coin is dropped from the
Leaning Tower of Pisa and falls freely from rest. What are its position and
velocity after 1.0 s, 2.0 s, and 3.0 s?

7. A flowerpot falls off a windowsill
and falls past the window below. You may ignore air resistance. It takes the
pot 0.420 s to pass from the top to the bottom of this window, which is 1.90 m high.
How far is the top of the window below the windowsill from which the flowerpot
fell?

8. A juggler performs in a room whose
ceiling is 3.0 m above the level of his hands. He throws a ball upward so that
it just reaches the ceiling. (a) What is the initial velocity of the ball? (b)
What is the time required for the ball to reach the ceiling? At the instant
when the first ball is at the ceiling, the juggler throws a second ball upward
with two-thirds the initial velocity of the first. (c) How long after the
second ball is thrown do the two balls pass each other? (d) At what distance
above the juggler’s hand do they pass each other?

9.A physics teacher performing an
outdoor demonstration suddenly falls from rest off a high cliff and
simultaneously shouts “Help.” When she has fallen for 3.0 s, she hears the echo
of her shout from the valley floor below. The speed of sound is (a) How tall is
the cliff? (b) If air resistance is neglected, how fast will she be moving just
before she hits the ground? (Her actual

speed will be less than this, due to
air resistance.)

10

**.**A helicopter carrying Dr. Evil takes off with a constant upward acceleration of Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for 10.0 s, Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off, and ignore the effects of air resistance.
(a) What is the maximum height above ground
reached by the helicopter?

(b) Powers deploys a jet pack strapped
on his back 7.0 s after leaving the helicopter, and then he has a constant
downward acceleration with magnitude How far is Powers above the ground when
the helicopter crashes into the ground?