Two ship leave port at the same time one travel at 5km/h on a bearing of 046 the other travel 9km/h on a bearing of 127 how far apart are the ship after 2 hours
All angles are measured CW from +y-axis.
AB = 5km/h * 2h = 10km[46o].
BA = 10km[46+180] = 10km[ 226o].
AC = 9km/h * 2h = 18km[127o].
BC = distance between the ships after 2h.
BC = BA+AC = 10[226] + 18[127]
BC = (10*sin226+18*sin127) + (10*cos226+18*cos127)i
BC = 7.2 - 17.8i
BC = sqrt(7.2^2 + 17.8^2) =
Diagram pls
Two ship leave port at the same time one travel at 5km/h on a bearing of 046 the other travel 9km/h on a bearing of 127 how far apart are the ship after 2 hours
Help me with it with diagram
You do not sail on a "bearing". You sail on a "heading". A bearing is a direction you look at another ship or a lighthouse or whatever. " That tanker bears south by Southwest for example. Math texts drive me nuts. Landlubbers.
Anyway:
first ship east (+x) distance = 10 cos 46 = 6.95 km
first ship north (+y) distance = 10 sin 46 = 7.19 km
180 - 127 = 53 degrees north of west
second ship east distance = -18 cos 53 = - 10.8 km
second ship north distance = 18 sin53 = 14.4 km
difference east-west = 6.95 + 10.8 =
difference north south = 14.4 - 7.9 =
you want the square root of the squares of those two numbers
Thanks but can you help me with the diagram please
To find the distance between the two ships after 2 hours, we can use the concept of relative velocity.
1. First, let's find the individual positions of the two ships after 2 hours:
- Ship 1: Traveling at 5 km/h on a bearing of 046, we can calculate the distance it travels in 2 hours by using the formula: Distance = Speed × Time. So, Distance1 = 5 km/h × 2 hours = 10 km.
- Ship 2: Traveling at 9 km/h on a bearing of 127, we can calculate the distance it travels in 2 hours by using the formula: Distance = Speed × Time. So, Distance2 = 9 km/h × 2 hours = 18 km.
2. Next, we need to find the relative position between the two ships. This can be done by finding the horizontal and vertical components of their positions.
- For Ship 1: The horizontal component of the position can be calculated using the formula: Horizontal Component = Distance × sin(Bearing). So, Horizontal1 = 10 km × sin(46°).
- For Ship 2: The horizontal component of the position can be calculated using the formula: Horizontal Component = Distance × sin(Bearing). So, Horizontal2 = 18 km × sin(127°).
3. Now, we need to find the vertical components of their positions.
- For Ship 1: The vertical component of the position can be calculated using the formula: Vertical Component = Distance × cos(Bearing). So, Vertical1 = 10 km × cos(46°).
- For Ship 2: The vertical component of the position can be calculated using the formula: Vertical Component = Distance × cos(Bearing). So, Vertical2 = 18 km × cos(127°).
4. Finally, we can find the distance between the two ships using the Pythagorean theorem, which states that the square of the hypotenuse (distance between the ships) is equal to the sum of the squares of the other two sides (horizontal and vertical components).
- Distance between the ships = √((Horizontal2 - Horizontal1)^2 + (Vertical2 - Vertical1)^2).
Now, substitute the values obtained in steps 1-3 into the distance formula to calculate the distance between the ships after 2 hours.