Match the term with its definition

A vector A has a magnitude of 5 units and points in the −y-direction, while a vector B has triple the magnitude of A and points

Harman [31]

Answer:

A+B; 5√5 units, 341.57°

A-B; 5√5 units, 198.43°

B-A; 5√5 units, 18.43°

Explanation:

Given A = 5 units

By vector notation and the axis of A, it is represented as -5j

B = 3 × 5 = 15 units

Using the vector notations and the axis, B is +15i. The following vectors ate taking as the coordinates of A and B

(a) A + B = -5j + 15i

A+B = 15i -5j

|A+B| = √(15)²+(5)²

= 5√5 units

∆ = arctan(5/15) = 18.43°

The angle ∆ is generally used in the diagrams

∆= 18.43°

The direction of A+B is 341.57° based in the condition given (see attachment for diagrams

(b) A - B = -5j -15i

A-B = -15i -5j

|A-B|= √(15)²+(-5)²

|A-B| = √125

|A-B| = 5√5 units

The direction is 180+18.43°= 198.43°

See attachment for diagrams

(c) B-A = 15i -( -5j) = 15i + 5j

|B-A| = 5√5 units

The direction is 18.43°

See attachment for diagram

5 0

3 years ago

Consider two laboratory carts of different masses but identical kinetic energies and the three following statements. I. The one

kolbaska11 [484]

Answer:

d) I and III only.

Explanation:

Let be $m_{1}$ and $m_{2}$ the masses of the two laboratory carts and let suppose that $m_{1} > m_{2}$ . The expressions for each kinetic energy are, respectively:

$K = \frac{1}{2}\cdot m_{1}\cdot v_{1}^{2}$ and $K = \frac{1}{2}\cdot m_{2}\cdot v_{2}^{2}$ .

After some algebraic manipulation, the following relation is constructed:

$\frac{m_{1}}{m_{2}} = \left(\frac{v_{2}}{v_{1}}\right)^{2}$

Since $\frac{m_{1}}{m_{2}} > 1$ , then $\frac{v_{2}}{v_{1}} > 1$ . That is to say, $v_{1} < v_{2}$ .

The expressions for each linear momentum are, respectively:

$p_{1} = \frac{2\cdot K}{v_{1}} = m_{1}\cdot v_{1}$ and $p_{2} = \frac{2\cdot K}{v_{2}} = m_{2}\cdot v_{2}$

Since $v_{1} < v_{2}$ , then $p_{1} > p_{2}$ . Which proves that statement I is true.

According to the Impulse Theorem, the impulse needed by cart I is greater than impulse needed by cart II, which proves that statement II is false.

According to the Work-Energy Theorem, both carts need the same amount of work to stop them. Which proves that statement III is true.

6 0

3 years ago

What is the wavelength of a 1200 Hz sound wave?

blagie [28]

Answer:

50cm

Explanation:

im honestly guessing

3 0

3 years ago

The electric field near the surface of Earth points downward and has a magnitude of 152 N/C. What is the ratio of the magnitude

VladimirAG [237]

Answer:

$2.7\times 10^{12}$

Explanation:

We are given that

Electric field = $E=152N/C$

We have to find the ratio of magnitude of the upward electric force on an electron to the magnitude of gravitational force on the electron.

We know that

F=qE

Charge on an electron,q= $1.6\times 10^{-19}C$

Using the formula

Upward electric force= $152\times 1.6\times 10^{-19}$ N

Upward electric force= $F_e=2.43\times 10^{-17}$ N

Mass of electron= $m_e=9.1\times 10^{-31} kg$

$g=9.8m/s^2$

Gravitational force= $F=mg$

Using the formula

Gravitational force= $F_g=9.1\times 10^{-31}\times 9.8=8.92\times 10^{-30} N$

Ratio of Fe to the Fg= $\frac{2.43\times 10^{-17}}{8.92\times 10^{-30}}$

$\frac{F_e}{F_g}=2.7\times 10^{12}$

8 0

3 years ago

Which of the following is not a way that oil production could potentially affect aquatic viability?

zaharov [31]

Since you have not presented any choices that would tell us which is NOT a way that oil production could potentially affect aquatic viability, I'll just go ahead and answer what are ways that oil could affect aquatic viability.

<span>-Offshore drilling contaminates and disturbs habitats of aquatic creatures
-Transport of oil across seas or oceans might lead to oil spill
-Waste products from energy factories using oil still would disturb habitat</span>

4 0

3 years ago

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