So apparently I suck at physics, because I don\'t understand any of this. Could

Question

So apparently I suck at physics, because I don't understand any of this.

Could you please show your work and explain if anything needs explaination. THANK YOU SO MUCH!

A army recruit on training walks due water for 5 miles, then in a northeasterly direction walks for 4 miles, and finally due north for 3 miles. How far will be from where he start? Consider an airplane moves In the sky per these vectors: Find the Resultant displacement vector? Answer 17.8'. SOI miles For these vectors A Projectile Motion: A rocket is aimed 70* to the sky and shot off with a initial velocity of 100 m/s. What is the total time it takes to come back to earth? How far does the rocket travel before hitting earth? How high does the rocket go in the earth's atmosphere? answers: t=l9.18s; distance: 655.96 m; moximum height: 1802.57 m

Explanation / Answer

1)

x direction:

x = -5 + 4*cos(45) = -2.1716 mi

y direction:

y = 4 sin45 + 3 = 5.8284 mi

==> r = sqrt(x^2 + y^2) = sqrt(2.1716*2.1716+5.8284*5.8284) = 6.2 mi

2)

x = 120*cos30 + 50*cos0 + 700*cos210 + 400*cos90 = -477.29 mi

y = 120*sin30 + 50*sin0 + 700*sin210 + 400*sin90 = 153.301 mi

==> r = sqrt(x^2 + y^2) = sqrt(477.29*477.29 + 153.301*153.301) = 501 miles

==> theta = arctan(y/x) = arctan(153.301/477.29) = 17.8 degrees

3)

Ax = 6 * cos0 = 6

Ay = 6 * sin0 = 0

Bx = 12 * cos60 = 6

By = 12 * sin60 = 10.39

Cx = 9 * cos(-60) = 4.5

Cy = 9 * sin(-60) = -7.794

A+B+C:

x comonent of A+B+C = Ax + Bx +Cx = 6 + 6 + 4.5 = 16.5 m

y comonent of A+B+C = Ay + By +Cy = 0 + 10.39 - 7.794 = 2.596 m

==> r = sqrt(16.5*16.5 + 2.596*2.596) = 16.7 m

direction: theta = arctan(2.596/16.5) = 9.0 degrees

A+B-C:

x comonent of A+B-C = Ax + Bx - Cx = 6 + 6 - 4.5 = 7.5 m

y comonent of A+B-C = Ay + By - Cy = 0 + 10.39 + 7.794 = 18.184 m

==> r = sqrt(7.5*7.5 + 18.184*18.184) = 19.7 m

direction: theta = arctan(18.184/7.5) = 68 degrees

A - 2C:

x comonent of A-2C = Ax - 2 Cx = 6 - 2*4.5 = -3 m

y comonent of A-2C = Ay - 2 Cy = 0 - 2*(-7.794) = -15.588 m

==> r = sqrt(3*3 + 15.588*15.588) = 15.9 m

direction: theta = 180 - arctan(15.588/3) = 101 degrees

B - (A+C):

x comonent of B-(A+C) = Bx - (Ax +Cx) = 6 - (6 + 4.5) = -4.5 m

y comonent of B-(A+C) = By - (Ay +Cy) = 10.39 - (0 - 7.794) = 18.184 m

==> r = sqrt(4.5*4.5 + 18.184*18.184) = 18.7 m

direction: theta = 180 - arctan(18.184/4.5) = 104 degrees

-A - B - C:

x comonent of -A-B-C = -Ax - Bx - Cx = -6 - 6 - 4.5 = -16.5 m

y comonent of -A-B-C = -Ay - By - Cy = 0 - 10.39 + 7.794 = -2.596 m

==> r = sqrt(16.5*16.5 + 2.596*2.596) = 16.7 m

direction: theta = -(180 - arctan((-2.596)/(-16.5))) = -171 or 189 degrees

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