Vector problem (motion in a plane)

In summary: Hi Ash! Welcome to PF! :smile:If he waits until he is directly opposite a porch, at a 90 degree angle with respect to the sidewalk, he will hit the porch.
  • #1
Ash413
2
0

Homework Statement


A newspaper boy throws papers sideways onto the porches of his customers while riding his bicycle along the sidewalk. The sidewalk is 15m in front of the porches. The boy throws the papers at a horizontal speed of 6m/s relative to himself, and rides the bicycle at a speed of 4m/s relative to the sidewalk.
Question: If he waits until he is directly opposite a porch, at what horizontal angle with respect to the sidewalk will he have to throw the paper to hit the porch?


Homework Equations


None really except for knowing how sine, cos and tan work.


The Attempt at a Solution


I did part a) and b) of this question. The full solution can be found here (Q. 159, solutions are at the end of the page): http://chatt.hdsb.ca/~irhs/irhs_web...nematics Extra Study Questions.pdf?Plugin=Box

I don't understand how they made the last triangle (for part c.), specifically how they labeled one side "4m/s" and how they knew it was a right triangle.
If you have a separate solution please share :)
Thanks!
Ash
 
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  • #2
Hi Ash! Welcome to PF! :smile:
Ash413 said:
If he waits until he is directly opposite a porch …

I don't understand how they made the last triangle (for part c.), specifically how they labeled one side "4m/s" and how they knew it was a right triangle.

In the diagram, horizontal represents the line of the road, so the horizontal side of 4 represents the 4m/s of the bike relative to the ground.

The vertical line represents the route that the newspaper actually takes (at an unknown speed) … it goes perpendicular to the road, since the newspaper is directly opposite the porch when it is thrown :wink:
 
  • #3
tiny-tim said:
Hi Ash! Welcome to PF! :smile:


In the diagram, horizontal represents the line of the road, so the horizontal side of 4 represents the 4m/s of the bike relative to the ground.

The vertical line represents the route that the newspaper actually takes (at an unknown speed) … it goes perpendicular to the road, since the newspaper is directly opposite the porch when it is thrown :wink:

Thank you sooo much :biggrin: I finally see it!
Ash
 

1. What is a vector problem in terms of motion in a plane?

A vector problem in motion in a plane refers to a situation where an object's motion is described using both magnitude (size) and direction. This is represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction of motion.

2. How do you represent a vector in a plane?

A vector in a plane is typically represented using coordinates or components. The x-component represents the horizontal component of the vector and the y-component represents the vertical component of the vector. These components can be used to calculate the magnitude and direction of the vector.

3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude (size) and no direction. Examples of scalars include time, temperature, and mass. A vector, on the other hand, has both magnitude and direction. Examples of vectors include displacement, velocity, and force.

4. How do you add or subtract vectors in a plane?

To add or subtract vectors in a plane, you can use the head-to-tail method. This involves placing the tail of one vector at the head of another vector and drawing a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the sum of the original vectors.

5. What is the Pythagorean theorem and how is it used in vector problems?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In vector problems, this theorem can be used to calculate the magnitude of the resultant vector when two vectors are added together.

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