The duration is $T =72 \ years /tex]Explanation:From the question we are told that The distance is [tex]D = 35 \ light-years = 35 * 9.46 *10^{15} = 3.311 *10^{17} \ m$

Generally the time it would take for the message to get the the other civilization is mathematically represented as

$t = \frac{D}{c}$

Here c is the speed of light with the value $c = 3.08 *10^{8} \ m/s$

=> $t = \frac{3.311 *10^{17} }{3.08 *10^{8}}$

=> $t = 1.075 *10^9 \ s$

converting to years

$t = 1.075 *10^9 * 3.17 *10^{-8}$

$t = 34 \ years$

Now the total time taken is mathematically represented as

$T = 2* t + 2 + 2$

=> $T = 2* 34 + 2 + 2$

=> [tex]T =72 \ years /tex]

4 0

3 years ago

Consider the three dip1acement vectors A = (3i - 3j) m, B = (i-4j) m, and C = (-2i + 5j) m. Use the component method to determin

tia_tia [17]

Answer with Explanation:

We are given that

A=3i-3j m

B=i-4 j m

C=-2i+5j m

a. $D=A+B+C$

$D=3i-3j+i-4j-2i+5j$

$D=2i-2j$

Compare with the vector r=xi+yj

We get x=2 and y=-2

Magnitude= $\mid D\mid=\sqrt{x^2+y^2}=\sqrt{(2)^2+(-2)^2}=2\sqrt 2$ units

By using the formula $\mid r\mid=\sqrt{x^2+y^2}$

Direction: $\theta=tan^{-1}\frac{y}{x}$

By using the formula

Direction of D: $\theta=tan^{-1}(\frac{-2}{2})=tan^{-1}(-1)=tan^{-1}(-tan45^{\circ})=-45^{\circ}$

b.E=-A-B+C

$E=-3i+3j-i+4j-2i+5j$

$E=-6i+12j$

$\mid E\mid=\sqrt{(-6)^2+(12)^2}=13.4$ units

Direction of E= $\theta=tan^{-1}(\frac{12}{-6}=tan^{-1}(-2)=-63.4^{\circ}$

4 0

3 years ago