Vector Application Handout (First one to answer correctly gets brainest)

1. 50·√2·i - 50·√2·j

2. The magnitude is 220.49 pounds, the direction 16.7°

3. 197.9 N

4. The resultant speed is  778.31 km/hr

The true course of the plane is 27.72°

5. The direction of the boat is 354.315°

The speed of the boat is 34.19 knot

Step-by-step explanation:

1. Given that the airplane is descending at 100 mph at an angle 45° below the horizontal, we have;

Horizontal component = 100 × cos(45°) = 100 × (√2)/2 = 50·√2 mph

The vertical component = 100 × sin(-45°) = 100 × (-√2)/2 = -50·√2 mph

Which gives;

50·√2·i - 50·√2·j

2. The given forces are;

F₁ = 250 pounds at 25° with the horizontal

F₁ₓ = 250 × cos(25°) = 226.58 pounds

= 250 × sin(25°) = 105.655 pounds

F₂ = 45 pounds at 250° with the horizontal

F₂ₓ = 45 × cos(250°) = -15.39 pounds

= 45 × sin(250°) = -42.29 pounds

The magnitude of the resultant force F = √((F₁ₓ - F₂ₓ)² + ( - )²)

  F = √((226.58  + (-15.39))² + (105.655 + (-42.29))²)

  F = √(211.19)² + (63.365)²) = 220.49 pounds

The direction of the resultant force θ =

3. The horizontal force = 120 × cos(60°) + 180 × cos(40°) = 197.9 N

4. Direction of airplane = 30° North of East. we have;

Speed of airplane, = 724 km/hr

The x component of the speed of the airplane, = 724 × cos(30°) = 627 km/hr

The y component of the speed of the airplane, = 724 × sin(30°) = 362 km/hr

The wind speed, =   = 62 km/hr

The resultant speed in the x direction, Sₓ =   +   = 627 + 62 = 689 km/hr

The resultant speed in the y direction, = 362 km/hr

The magnitude of the resultant speed, S = √(Sₓ² + ²) = √(689² + 362²) = 778.31 km/hr

The direction of the airplane  θ =

5. The x,  and y, components of the speed of the yacht are;

= 20×sin(185°) = -1.743 knots

=  20×cos(185°) = -19.924 knots

The x, and y, components of the speed of the yacht are;

= 15×sin(290°) = -14.1 knots

=  15×cos(290°) = 5.13 knots

The resultant x, , and y,   are found as follows;

= + = -19.924  + -14.1 = -34.024 knots

=  + = -1.743 + 5.13 = 3.387

The resultant speed is given by the relation;

S =√(²  + ²) = √((-34.024)^2  + 3.387^2) = 34.19 knot

The direction of the boat, θ =

The direction of the boat = -5.685 = 354.315°

The speed of the boat = 34.19 knot.

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft

answer:

3 bags of apples and 2 bags of oranges.

step-by-step explanation: