1. While exploring a cave, a spelunker starts at the entrance and moves the following
distances in horizontal plane. She goes 50.0 m West, 150 m North, 80 m 60 ° S of E.
a) Draw the figure applying polygon method. (scale 40 m: 1 cm)
b) Find her resultant displacement from the cave entrance applying component method
2. Given: A = 2iƸ− 4jƸ B = −4iƸ+ 5jƸ− 2k. Find a) A•B b) B –A c) A+B d) A x B
e) angle between A and B
3. Given: r
Ԧ t = −2.0 cm + 0.4
cm
s
2
t
2
iƸ+ 3.0
cm
s
tjƸ
For the time interval from t = 2 to t = 6.0 s, find a)displacement b) average velocity
c) average acceleration
4. An object is thrown upward from a height of 60.0 m above ground, with a speed of 8.0
m/s. How high will the object rise? How long will it take the object reach the ground? What
is the object’s velocity upon hitting the ground? Where is the object and what is its velocity
2 s after it was thrown?
5. A ball is rolled on a flat surface with an initial velocity of 1.50 m/s and speeds up at a rate
of 0.8 m/s
2
. What is the ball’s velocity at a distance 5 m? How long will the ball travel to
attain a velocity of 15 m/s?
6. A projectile is launched, 10.0 m above the ground, with a velocity of 25.0 m/s at an
angle 40 above the horizontal. Determine the location and velocity of the projectile 2.0 s
after launch. Is the projectile still on its way up or already on its way down at that location?
1. To draw the figure using the polygon method:
- Start by drawing a line to represent the spelunker's initial position at the cave entrance.
- Move 50.0 m to the west from the initial position and draw another line representing this movement.
- From the end of the previous line, move 150 m to the north and draw another line.
- Finally, from the end of the previous line, move 80 m at an angle of 60 degrees south of east and draw the final line. This line will be shorter and angled towards the south of the initial position.
To find the resultant displacement using the component method:
- Convert the given distances into their respective x and y components.
- 50.0 m west would have an x-component of -50.0 m and a y-component of 0 m.
- 150 m north would have an x-component of 0 m and a y-component of 150 m.
- 80 m 60° S of E can be split into x and y components by using trigonometry. The x-component would be 80 m * cos(60°) and the y-component would be -80 m * sin(60°).
- Add up the x-components and y-components separately.
- The resultant displacement can be found by taking the square root of the sum of the squares of the x-component and y-component.
2. a) To find the dot product of A and B:
- The dot product of two vectors can be calculated by taking the product of their corresponding components and then summing up the products.
- For A and B: A • B = (2 * -4) + (-4 * 5) + (0 * -2).
b) To find B - A:
- Subtract the corresponding components of vector A from vector B.
- B - A = (-4 - 2)i + (5 - (-4))j + (-2 - 0)k.
c) To find A + B:
- Add the corresponding components of vectors A and B together.
- A + B = (2 - 4)i + (0 + 5)j + (0 - 2)k.
d) To find the cross product of A and B:
- The cross product of two vectors is a vector that is perpendicular to both of the original vectors.
- For A and B: A x B = (4 * (-2))i + ((-4) * (-2))j + ((-4) * 5)k.
e) To find the angle between A and B:
- The angle θ between two vectors A and B can be calculated using the dot product formula: A • B = |A| |B| cos(θ).
- Rearrange the formula to solve for θ: θ = arccos((A • B) / (|A| |B|)).