Physics 011
Chapter 3: Kinematics in Two Dimensions; Vectors
MC#3A



1. 

A car
travels due east for a distance of 3 miles and then due north for an
additional 4 miles before stopping. What is the shortest straight line
distance between the starting and ending points of this trip? See Section 32 




2. 

A car
travels due east for a distance of 3 miles and then due north for an
additional 4 miles before stopping. What is the angle a of the
shortest path relative to due north? See Section 34 




3. 

A vector A
makes an angle of 60° with the x axis of a Cartesian coordinate system. Which
of the following statements is true of the indicated magnitudes? See Section 34 




4. 

Force is a
vector quantity measured in units of newtons, N. What must be the angle
between two concurrently acting forces of 5 N and 3 N respectively if the
resultant vector is 8 N? 




5. 

Two
forces, A and B, act concurrently on an object. Both vectors
have the same magnitude of 10 N and act at right angles to each other. What
is the closest estimate of their resultant? 




6. 

For which
of the vector diagrams is it true that T_{1} + T_{2}
= T_{3}? See Section 32 




7. 

For which
of the vector diagrams is it true that T_{1}  T_{2}
= T_{3}? 




8. 

For which
of the vector diagrams is it true that T_{1} + T_{2}
+ T_{3} = 0? See Section 32 




9. 

For which
of the vector diagrams is it most obviously true that T_{1} + T_{2}
+ T_{3} 0? See Section 32 




10. 

For which
of the vector diagrams is it true that T_{1} + T_{3}
=  T_{2}? See Section 32 




11. 

For which
of the vector diagrams is it true that T_{1}^{2} + T_{2}^{2}
= T_{3}^{2}? See Section 32 




12. 

Which of
the following sets of displacements, if they were oriented any way you wish,
could not be made to yield a zero net displacement? See Section 32 




13. 

An
airplane is flying in the presence of a 100 km/h wind directed due north.
What must be the velocity and heading of the plane if it is to maintain a
velocity of 500 km/h due east with respect to the ground? 




14. 

A quarterback
throws a football with a velocity of 7 m/s and an angle of 15° above the
horizontal. How far away should the designated receiver be? See Section 36 




15. 

What must be
the minimum velocity of a projectile launched from ground level over a flat,
horizontal if it is to strike a target 100 meters away? See Section 36 




16. 

An arrow
is shot at an angle of 30° above the horizontal with a speed of 29.4 m/s. How
long will it take for the arrow to strike the ground? See Section 36 




17. 

At what
angle should a projectile be fired in order for its range to be at maximum? See Section 36 




18. 

A bomber
is traveling due east with a velocity of 300 m/s when it releases a bomb. If
the bomb takes 2.00 seconds to strike the ground, what was the range
(horizontal distance) of the bomb's path? 




19. 

A bomber
is flying with a velocity of 500 km/h at an altitude of 1960 meters when it
drops a bomb. How long does it take for the bomb to hit the ground? See Section 36 




20. 

A ball is thrown
from the roof of a tall building with a horizontal velocity of 6.0 m/s. What
is its speed after 3.0 seconds of flight? See Section 36 




21. 

A
projectile is fired at an angle above the horizontal. The air resistance is
negligible. The initial horizontal velocity component is twice that of the
initial vertical velocity component. The trajectory of the missle is best
described as See Section 36 




22. 

Which
trajectory best describes a ball rolling down a curved ramp that ends at
point P?
See Section 35 




23. 

A cannon
is placed on a flatcar of a train. The train is moving with a uniform speed
5.0 m/s when the cannon fires a ball vertically up at 10 m/s. Which vector
best represents the velocity of the cannon ball as seen by a man standing on
the ground? 




24. 

A bullet
is fired from a gun with a muzzle velocity of 300 m/s and at an angle of 30°
above the horizontal. What is the magnitude of the vertical component of the
muzzle velocity? 




25. 

Assume
that the magnitude of the acceleration of gravity is exactly 10.0 m/s^{2}
and that there is no friction with the air. A bored golfer standing on a
flat, horizontal section of the golf course hits a small stone with his club
so that the horizontal and vertical components of its velocity as it leaves
the ground are 20.0 m/s and 15.0 m/s respectively. When the stone is at the top of its trajectory, its speed is ___ m/s. See Section 35 




26. 

Assume
that the magnitude of the acceleration of gravity is exactly 10.0 m/s^{2}
and that there is no friction with the air. A bored golfer standing on a
flat, horizontal section of the golf course hits a small stone with his club
so that the horizontal and vertical components of its velocity as it leaves
the ground are 20.0 m/s and 15.0 m/s respectively. When the stone is at the top of its trajectory, the magnitude of its
acceleration is ___ m/s^{2}. See Section 35 




27. 

Assume
that the magnitude of the acceleration of gravity is exactly 10.0 m/s^{2}
and that there is no friction with the air. A bored golfer standing on a
flat, horizontal section of the golf course hits a small stone with his club
so that the horizontal and vertical components of its velocity as it leaves
the ground are 20.0 m/s and 15.0 m/s respectively. The time required for the stone to reach the highest point in its
trajectory is ___ s. 




28. 

Assume
that the magnitude of the acceleration of gravity is exactly 10.0 m/s^{2}
and that there is no friction with the air. A bored golfer standing on a
flat, horizontal section of the golf course hits a small stone with his club
so that the horizontal and vertical components of its velocity as it leaves
the ground are 20.0 m/s and 15.0 m/s respectively. The horizontal distance traveled by the stone before it hits the ground is
___ m. See Section 35 




29. 

A
projectile is launched from ground level with speed v_{o} at an angle
_{o}
above the horizontal. If v_{o} was increased slightly, the range of the projectile would
___. See Section 35/36 




30. 

A
projectile is launched from ground level with speed v_{o} at an angle
_{o}
above the horizontal. If _{o}
was increased slightly, the time the projectile spends in the air before
hitting the ground would ___. See Section 35/36 




31. 

A
projectile is launched from ground level with speed v_{o} at an angle
_{o}
above the horizontal. If v_{o} was increased slightly, the maximum height attained by
the projectile would ___. See Section 35/36 




32. 

A
projectile is launched from ground level with speed v_{o} at an angle
_{o}
above the horizontal. If _{o}
was decreased slightly, the range of the projectile would ___. 
