Question
1. Vector A has a magnitude of29.5units and it points in a direction345counterclockwise from the positive x -axis.What are the x -and y -componentsof A
1. Vector A has a magnitude of29.5units and it points in a direction345counterclockwise from the positivex-axis.What are thex-andy-componentsof A?
Ax= units
Ay= units
2. A vector A has components Ax=2.00m and Ay=4.00m.
Find the magnitude (in m) and the direction (in degrees counterclockwise from the +x-axis) of the vector.
magnitude m
direction counterclockwise from the +x-axis
3. The brakes are applied to a moving car, causing it to uniformly slow down. While slowing, it moves a distance of 40.0 m in 7.80 s to a final velocity of 1.75 m/s, at which point the brakes are released.
(a)What was its initial speed (in m/s), just before the brakes were applied? m/s
(b)What was its acceleration (in m/s2) while the brakes were applied? (Assume the initial direction of motion is the positive direction. Indicate the direction with the sign of your answer.) m/s2
4. A speedboat increases its speed uniformly from
vi=20.0m/s to vf=29.0m/s in a distance of x=1.90102m.
(a) Draw a coordinate system for this situation and label the relevant quantities, including vectors.
(b) For the given information, what single equation is most appropriate for finding the acceleration?
a=
vfvi |
tfti |
x=vit+
1 |
2 |
at2
vf=vi+at
vf2=vi2+ 2a(x)
(c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms ofvf,vi, andx. a =
(d) Substitute given values, obtaining the acceleration. m/s2 (e) Find the time it takes the boat to travel the given distance. s
5. A solid metal ball is thrown directly downward, with an initial speed of 8.15 m/s, from the top of a structure at a height of 30.2 m. How much time (in s) does it take before striking the ground?
s
6. The figure below shows two boxes connected to each other by a light rope that passes over a pulley with negligible friction. The box of mass
m1=5.50kg
lies on a horizontal table with negligible friction, while the box of mass
m2=10.4kg
hangs vertically. Two boxes labeledm1andm2are attached together by a rope.
- Boxm1lies on a horizontal table with the rope extending horizontally from its right side.
- The rope extends horizontally from the right side ofm1then goes over a pulley and then straight down tom2.
- Boxm2hangs from the rope.
(a)What is the magnitude of the acceleration of each box (in m/s2)? (Here,
a1
is the acceleration of
m1,
and
a2
is the acceleration of
m2.)
a1
= m/s2
a2
= m/s2(b)What is the tension in the rope (in N)? N
7. Atwood's machine (see the figure below) consists of two masses: one of mass 4.23 kg and the other of mass 11.0 kg. When released from rest, what is the acceleration of the system? (Enter the magnitude in m/s2.)
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