Motion in a Plane: Solving Velocity & Speed Problems

In summary, we are given a problem where a cargo ship carrying 50 tons of coffee is initially traveling North with a speed of 40 m/s. Five minutes later, the ship is traveling at 20 m/s into San Francisco Bay in a direction 48 degrees North of East. Using a coordinate system with +x corresponding to East and +y corresponding to North, we are asked to find the x and y components of the initial and final velocity, as well as the change in magnitude and direction of the ship's velocity. To do this, we can use trigonometry to separate the velocity into "east" and
  • #1
marisa29
6
0
Have no idea how to start this probelm if anybody could help thank you

Homework Statement


A cargo ship carrying 50 tons of coffee is initially traveling North with a speed of 40 m/s. Five minutes later, the cargo ship is traveling at 20 m/s into san Fransico bay in a direction 48 degress North of East. Use a coordinate system with + x corresponding to East and +y corresponding to North to answer the following question

a) What are the x and y components of the initial velocity?

B) what are the x and y componenets of the final velocity?

C) What is the change in velocity (magnitude and direction) of the ship?

D) explain the difference b/w velocity and speed?



Homework Equations



a) No clue
B) cos0=a/h
sin0= o/h
C) delta (r)/delta(t) and to get delta r i use c^2= B^2 + C^2



The Attempt at a Solution



a) x=0 y= 40 m/s
B)
C)

If i have the equations right i don't know what to use for o and a
 
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  • #2
marisa29 said:
Have no idea how to start this probelm if anybody could help thank you

Homework Statement


A cargo ship carrying 50 tons of coffee is initially traveling North with a speed of 40 m/s. Five minutes later, the cargo ship is traveling at 20 m/s into san Fransico bay in a direction 48 degress North of East. Use a coordinate system with + x corresponding to East and +y corresponding to North to answer the following question

a) What are the x and y components of the initial velocity?
In other words separate the volocity into "east" and "north" components.

B) what are the x and y components of the final velocity?

C) What is the change in velocity (magnitude and direction) of the ship?

D) explain the difference b/w velocity and speed?



Homework Equations



a) No clue
B) cos0=a/h
sin0= o/h
C) delta (r)/delta(t) and to get delta r i use c^2= B^2 + C^2



The Attempt at a Solution



a) x=0 y= 40 m/s
Yes, of course! why did you say "no clue"?

B)
Draw a picture. You are told the velocity is "20 m/s into san Fransico bay in a direction 48 degress North of East." so draw a line 20 units long at 48 degrees above the x-axis (East). Draw a line from the end of that perpendicular to the x-axis so you have a right triangle with angle 48 degrees and hypotenuse 20 units long. The "near" side is the x (East) component and the y (North) component is the "opposite" side of the right triangle. Now use the trig functions you cited above to find those lengths.

C)
The speed changed from "40 m/s" to "20 m/s". How much change is that? The angle changed from "North" to "48 degrees North of East". How much change is that? You picture might help.

For (D) you probably can look up the definitions of "velocity" and "speed" in your textbook.

If i have the equations right i don't know what to use for o and a
 
  • #3
so does it look like this ? Thanx for the help
__ _ /_|
__ /___|_40 m/s *=48 degress
20/____|
_ / *___|

x component is 20m/s*cos(48)=13.38
y component is 20 m/s*sin(48)=14.86

P.s couldn't get it to look like a triangle /_|
 
Last edited:

FAQ: Motion in a Plane: Solving Velocity & Speed Problems

1. What is the difference between velocity and speed?

Velocity is a vector quantity that describes the rate of change of an object's position in a specific direction, whereas speed is a scalar quantity that describes the rate of change of an object's distance traveled regardless of direction.

2. How do you calculate average velocity?

Average velocity can be calculated by dividing the change in an object's displacement by the change in time. This can be represented by the equation: average velocity = (final displacement - initial displacement) / time interval.

3. What is the difference between average velocity and instantaneous velocity?

Average velocity refers to the average rate of change of an object's position over a given time interval, while instantaneous velocity refers to the rate of change of an object's position at a specific moment in time.

4. How do you solve for displacement using velocity and time?

To solve for displacement using velocity and time, you can use the formula: displacement = velocity x time. This formula assumes that the object is moving at a constant velocity.

5. Can an object have a constant speed but changing velocity?

Yes, an object can have a constant speed but changing velocity if its direction of motion is changing. This can occur when an object is moving in a circular path, where its speed remains constant but its velocity changes as it changes direction.

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