physics 111 hw4
assigned 14 September 2011
2DCA-02. Firemen are shooting a stream of water at a burning building using a highpressure hose that shoots out the water with a speed of 25.0 m/s as it leaves the end of
the hose. Once it leaves the hose, the water moves in projectile motion. The firemen
adjust the angle of elevation α of the hose until the water takes 3.00 s to reach a
building 45.0 m away. You can ignore aire resistance, and assume that the end of the
hose is at ground level.
a) Find the angle of elevation α.
b) Find the speed and acceleration of the water at the highest point in its trajectory.
c) How high above the ground does the water strike the building, and how fast is it
moving just before it hits the building?
2DCA-03. An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0o above
the horizontal. When the plane is 114 m directly above a dog that is standing on level
ground, a suitcase drops out of the luggage compartment. How far from the dog will
the suitcase land? You may ignore air resistance.
2DCA-05. A baseball thrown at an angle of 60.0o above the horizontal strikes a building
18.0 m away at a point 8.00 m above the point from which it is thrown. Ignore air
resistance.
a) Find the magnitude of the initial velocity of the baseball (the velocity with which
the baseball is thrown).
b) Find the magnitude and direction of the velocity of the baseball just before it
strikes the building.
c) Sketch x vs. t, y vs. t, vx vs t, and vy vs t graphs of the motion.
2DCA-07. A cannon sits at the edge of a vertical cliff that overlooks a flat valley. The
nozzle of the cannon is a height h above the valley floor. If the cannon shoots a
cannonball horizontally off the cliff with speed vi, derive an expression for the
horizontal distance d the ball lands from the cliff wall on the valley floor in terms of
vi and h.
RA-01. A car going N makes a 90o turn to the E. It traces out ¼ of a circle with radius
25 m as it makes the turn. At the start of the turn it is going 6 m/s N. At the end of
the turn it is going 8 m/s E. The magnitude of the tangential acceleration during the
turn is constant, but, of course, the direction is not.
a) Find the average velocity for the turn.
b) Find the average acceleration for the turn.
c) Find the instantaneous acceleration at the midpoint of the turn.
RA-03. (Young & Friedman 11th ed. Ex. 3.33-4) A Ferris wheel with radius 14m is
turning about a horizontal axis through its center. The linear speed of a passenger on
(over)
the rim is constant and equal to 7.00 m/s. What are the
magnitude and direction of the passenger’s acceleration as
she passes through
a) the lowest point in her circular motion?
b) the highest point in her circular motion?
c) How long does it take the Ferris wheel to make one
revolution?
Now the same Ferris wheel is at rest, and just starts up. At
a given instant, a passenger on the rim of the wheel is
passing through the lowest point of her circular motion, is
moving at 3.00 m/s, and is gaining speed at a rate of 0.500
m/s2.
d) Find the magnitude and direction of the passenger’s acceleration at this instant.
RA-04. You start at rest at point A and travel in the path shown at
right with a constant linear/tangential acceleration of 0.4 m/s2 to
point B. What is
a) your average velocity for the A → B trip?
b) your average acceleration for the A → B trip?
c) your net instantaneous acceleration at point P, halfway around
the circular part?
(over)
A
10 m
10 m P
B