1. The components of a vector V can be written (Vx, Vy, Vz). What are the compon

Question

1. The components of a vector V can be written (Vx, Vy, Vz).
What are the components and length of a vector which is the sum of the two vectors, V1 and V2, whose components are (8.8,?3.7,0.0) and (4.0,?7.5,?4.1)?

a. Enter the x, y, and z components of the vector separated by commas.

b. What is the length of this vector?

Express your answer using three significant figures.

2. Vector V? 1 is 6.4 units long and points along the negative x axis. Vector V? 2 is 8.6 units long and points at 55? to the positive x axis.

a. What are the x and y components of vector V? 1?

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

b. What are the x and y components of vector V? 2?

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

c. Determine the magnitude of the sum V? 1+V? 2.

Express your answer using two significant figures.

d. Determine the angle of the sum V? 1+V? 2.

Express your answer using two significant figures.

3. What is the y component of a vector (in the xy plane) whose magnitude is 83.5 and whose x component is 68.7?

Express your answer numerically. If there is more than one answer, enter each answer separated by a comma.

4.

Part A

If Vx = 7.30 units and Vy = -8.10 units, determine the magnitude of V?

Part B

Determine the direction of V? .

5. The summit of a mountain, 2210m above base camp, is measured on a map to be 4170mhorizontally from the camp in a direction 36.6?west of north.

Part A

What are the components of the displacement vector from camp to summit? Choose the x axis east, y axis north, and z axis up.

Enter the x, y, and z components of the displacement vector separated by commas.

Part B

What is its magnitude?

6. A projectile is fired with an initial speed of 61.9m/s at an angle of 31.2? above the horizontal on a long flat firing range.

Part A

Determine the maximum height reached by the projectile.

Part B

Determine the total time in the air.

Part C

Determine the total horizontal distance covered (that is, the range).

Part D

Determine the speed of the projectile 1.32s after firing.

Part E

Determine the direction of the projectile 1.32s after firing.

Explanation / Answer

1)

a) ( 12.8 , -11.2 , -4.1 )

b) sqrt(12.8^2 + 11.2^2 + 4.1^2) = 17.495

2)

a) V1x = -6.4.....V1y = 0

b) V2x = 8.6*cos55 = 4.93

V2y = 8.6* sin55 = 7.04

( 4.93 , 7.04 )

c) V1 + V2 = (1.47 , 7.04 )

magnitude = sqrt(1.47^2 + 7.04^2) = 7.19

d) angle = tan^-1(Vy / Vx) = tan^-1(7.04/1.47) = 78.20

4)

A ) V = sqrt(Vx^2 +Vy^2) = 10.904

B) direction = 47.97 with +x axis in clock wise direction

5)

A) ( -4170*sin36.6 , 4170*cos36.6 , 2210 )

B) 4719.42

6)

A) H = vy^2/2g = (61.9*sin31.2)^2/(2*9.8) = 52.460 m

B) T= 2*Vy/g = (2*61.9*sin31.2)/9.8 = v s

C) X = Vx*T = 346.48

D) Vyf = Vy - gt = (61.9*sin31.2)-(9.8*1.32) = 19.129 m/s

Vx = 61.9*cos31.2 = 52.94 m/s

V = sqrt(52.94^2+ 19.129^2) = 56.28 m/s

E) direction = tan^-1(19.129/2.94) = 81.26

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