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 A x units A y units 2 A vector A has components A x 2 00m and A y 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 s 2 ) 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 s 2 4 A speedboat increases its speed uniformly from v i 20 0m s to v f 29 0m s in a distance of x 1 9010 2 m (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 v f v i t f t i x v i t 1 2 at 2 v f v i at v f 2 v i 2 2 a ( x ) (c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms of v f , v i , and x a (d) Substitute given values, obtaining the acceleration m s 2 (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 m 1 5 50kg lies on a horizontal table with negligible friction, while the box of mass m 2 10 4kg hangs vertically Two boxes labeled m 1 and m 2 are attached together by a rope Box m 1 lies on a horizontal table with the rope extending horizontally from its right side The rope extends horizontally from the right side of m 1 then goes over a pulley and then straight down to m 2 Box m 2 hangs from the rope (a)What is the magnitude of the acceleration of each box (in m s 2 ) (Here, a 1 is the acceleration of m 1 , and a 2 is the acceleration of m 2 ) a 1 m s 2 a 2 m s 2 (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 s 2 )

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Sep 27, 2024

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?

A_x= units

A_y= units

2. A vector A has components A_x=2.00m and A_y=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

v_i=20.0m/s to v_f=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?

v_fv_i

t_ft_i

x=v_it+

at²

v_f=v_i+at

v_f²=v_i²+ 2a(x)

(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?

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.)