+1904 Six word problems. Please show how you got your answer.
1) A ship leaves port on a bearing of 28° and travels 7.5 miles. The ship then turns due east and travels 4.1 miles. How far is the ship from the port and what is its bearing?
2) Two tow trucks are pulling on a truck stuck in the mud. Tow truck #1 is pulling with a force of 635 lbs at 51° from the horizontal while tow truck #2 is pulling with a force of 592 lbs at 39° from the horizontal. What is the magnitude and direction of the resultant force?
3) A boat is travelling at a speed of 30 mph. The vector that represents the velocity is \(15<\sqrt{2},-\sqrt{2}>\). What is the bearing of the boat?
4) A plane leaves the airport on a bearing 45° traveling at 400 mph. The wind is blowing at a bearing of 135° at a speed of 40 mph. What is the actual velocity of the plane?
5) A 700 lb force just keeps a 4000 lb box from sliding down a ramp. What is the angle of inclination of the ramp?
6) An airplane is flying in the direction 15° North of East at 550 mph. A wind is blowing in the direction 15° South of East at 45 mph.
a) Find the component form of the velocity of the airplane and the wind.
b) Find the actual speed ("ground speed") and direction of the airplane.
+128570 1. The distance from port can be found using the Law of Cosines
d^2 = 7.5^2 + 4.1^2 - 2(7.5)(4.1)cos(118)
d = sqrt [7.5^2 + 4.1^2 - 2(7.5)(4.1)cos(118)] = about 10.096 miles
It's bearing [ from port] is given by :
(90 - arctan[6.62/ 7.62 ] ) ° = [ 90 - 41]° = about 49°
Here's a pic :
+128570 3. The bearing of the boat is [90 + 45]° = 135°
Here's a pic :
+128570 4) A plane leaves the airport on a bearing 45° traveling at 400 mph. The wind is blowing at a bearing of 135° at a speed of 40 mph. What is the actual velocity of the plane?
The vector of the plane's path of travel and the wind vector are at right angles to each other......the resultant [the actual velocity] is give by :
sqrt [400^2 + 40^2] = about 402 mph
Here's a pic :
+128570 6) An airplane is flying in the direction 15° North of East at 550 mph. A wind is blowing in the direction 15° South of East at 45 mph.
a) Find the component form of the velocity of the airplane and the wind.
b) Find the actual speed ("ground speed") and direction of the airplane.
The components of the velocity of the plane are <550cos15, 550sin15>
The components of the wind velocity are < 45cos345, 45 sin345 >
The x components of the resultant = 550cos15 + 45cos345 = about 574.726
The y components of the resultant = 550sin15 + 45sin345 = about 130.7
So...the resultant ground speed = sqrt[ 574.726^2 + 130.7^2] = about 589.4 mph
