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andriy [413]
3 years ago
8

5. The analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions,

for which graphical work is inconvenient. Find the magnitude of the resultant of the vectors A = i12 —j37 + k58 and B = i5 + j30 — k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively
Physics
1 answer:
Gwar [14]3 years ago
6 0

Answer:

C = 17 i^ - 7 j^ + 16 k^ ,   | C| = 24.37

Explanation:

To work the vactor component method, we add the sum in each axis

C = A + B = (Aₓ + Bₓ) i ^ + (A_{y} + B_{y}) i ^ + (A_{z} + B_{z}) k ^

Cₓ = 12+ 5 = 17

C_{y} = -37 +30 = -7

C_{z} = 58 -42 = 16

Resulting vector

C = 17 i ^ - 7j ^ + 16k ^

The mangitude of the vector is

| C | = √ c²

| C | = √( 17² + 7² + 16²)

| C| = 24.37

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A stone is tossed horizontally from the highest point of a 95 m building and lands 105 m from the base of the building. Ignore a
aalyn [17]

Answer:

A) t = 4.40 s , B)   v = 23.86 m / s ,  c)  v_y = - 43.12 m / s , D)  v = 49.28 m/s

Explanation:

This is a projectile throwing exercise,

A) To know the time of the stone in the air, let's find the time it takes to reach the floor

          y = y₀ + v_{oy} t - ½ g t²

as the stone is thrown horizontally  v_{oy} = 0

          y = y₀ - ½ g t²

          0 = y₀ - ½ g t²

          t = √ (2 y₀ / g)

          t = √ (2 95 / 9.8)

          t = 4.40 s

B) what is the horizontal velocity of the body

          v = x / t

          v = 105 / 4.40

          v = 23.86 m / s

C) The vertical speed when it touches the ground

          v_y = v_{oy} - g t

          v_y = 0 - 9.8 4.40

          v_y = - 43.12 m / s

the negative sign indicates that the speed is down

D) total velocity just hitting the ground

          v = vₓ i ^ + v_y j ^

          v = 23.86 i ^ - 43.12 j ^

Let's use Pythagoras' theorem to find the modulus

          v = √ (vₓ² + v_y²)

          v = √ (23.86² + 43.12²)

           v = 49.28 m / s

we use trigonometry for the angle

          tan θ = v_y / vₓ

          θ = tan⁻¹ (-43.12 / 23.86)

            θ = -61

7 0
3 years ago
a 2.0 kg ball is dropped from a height of 20 m onto a soft surface and rebounds to a height of 5.0 m . what is the magnitude of
Yuki888 [10]

Based on the data provided, the impulse of the floor on the ball is 59.4 Ns.

<h3>What is the impulse of the floor on the ball?</h3>

Using the equation of motion to determine the velocity at the end of the fall

  • v^2 = u^2 + 2gh

Where v is velocity at the end of fall

u is initial velocity = 0

g is acceleration due to gravity = 9.81 m/s^2

h is height = 20

  • Taking downward velocity as negative and up as positive

v^2 = 0 + 2 (9.81)(20)

v^2 = 392.4

v = - 19.8 m/s

The velocity, v after bouncing is calculated also:

u = 0

g = 9.81 m/s^2

h = 5.0 m

v^2 = 0 + 2(9.81)(5)

v^2 = 98.1

v = 9.904 m/s

  • Impulse = change in momentum
  • Impulse = m(v- u)

Impulse = 2.0 × (9.9 -(-19.8)

Impulse = 59.4 Ns

Therefore, the impulse of the floor on the ball is 59.4 Ns.

Learn more about impulse at: brainly.com/question/904448

5 0
2 years ago
Kiana is wearing a black shirt and shiny necklace. While she is outside at recess her shirt absorbs the light waves and gets ver
makvit [3.9K]

Answer:

Black bodies are good absorber of light waves from the sun, while shining surfaces are good reflector of the light waves.

Explanation:

Generally, a black surface or material tends to absorb light waves while under the sun, while a shiny surface is a good reflector of the waves. This is because the black material is a good absorber, and also a good emitter.

The shiny necklace can only absorb little light waves from the sun, thus it reflects most of the light waves. The reflection is the reason for the small circles of light seen around the yard.

However, when in a cool environment the black shirt would cools faster (good emitter) than the shiny necklace.

4 0
2 years ago
1. What is weather?
Fynjy0 [20]
Weather is rain sun snow storm and warm and cold
6 0
3 years ago
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PLSSS HELP ITS URGENT ILL RATE YOU BRAINLIEST:) A truck whose bed is 4 m long, 2.2 m wide, and 1.0 m high is delivering sand for
natka813 [3]

Answer:

one truck load is 2.5*1.5*1 = 3.75m^3

7/3.75 = 1.86 loads,

so 2 trips must be made.

Explanation:

8 0
3 years ago
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