Two ships A&B leave port at same time the ship A is north-west at 32km/hr & ship B is 40degree south of west at 24 m/hr determine 1)the speed of ship B relative to ship A
2)At what time they will be 150km apart
1. A = 32km/h[135o],CCW
Xa = 32*cos135 = -22.63 km/h
Ya = 32*sin135 = 22.63 km/h
B = 24km/h[220o],CCW
Xb = 24*cos220 = -18.39 km/h
Yb = 24*sin220 = -15.43 km/h
Xa and Xb are in same direction. So we
subtract:
Xc=Xb-Xa = -18.39 - (-22.63)=4.24 km/h
Yc = Yb+Ya = -15.43 + 22.63 = 7.2 km/h
tanC = Yc/Xc = 7.2/4.24 = 1.69811
C = 59.5o
Vb=Yc/sinC = 7.2/sin59.5=8.36 km/h[59.5]
= Velocity of B relative to A.
To solve this problem, we need to break it down into two components: the relative speed of ship B with respect to ship A, and the time at which they will be 150 km apart.
1) The speed of ship B relative to ship A:
To determine the relative speed, we need to consider the vector components of each ship's velocity.
Ship A is moving northwest, which can be represented by two components: a northward component and a westward component. The northward component can be calculated using trigonometry, as the ship is moving in a 45-degree angle. So, the northward component of ship A's velocity is given by:
northward component = ship A's speed * cos(45°) = 32 km/hr * cos(45°)
Ship B is moving 40 degrees south of west, which means it has a westward component and a southward component. We need to find the westward component of ship B's velocity, which can be calculated using trigonometry. The westward component of ship B's velocity is given by:
westward component = ship B's speed * cos(40°) = 24 km/hr * cos(40°)
To find the speed of ship B relative to ship A, we subtract the westward component of ship A's velocity from the westward component of ship B's velocity:
speed of ship B relative to ship A = westward component of ship B - westward component of ship A
speed of ship B relative to ship A = 24 km/hr * cos(40°) - 32 km/hr * cos(45°)
2) Time at which they will be 150 km apart:
To determine the time at which they will be 150 km apart, we will use the formula:
distance = speed * time
Since the distance between the two ships is increasing, we can set up two equations, one for each ship:
distance covered by ship A = speed of ship A * time
distance covered by ship B = speed of ship B relative to ship A * time
We need to solve these two equations simultaneously to find the time at which they will be 150 km apart.
Substitute the values we calculated earlier into the equations:
32 km/hr * time = 150 km (Distance for ship A)
(speed of ship B relative to ship A) * time = 150 km (Distance for ship B)
Now, we have two equations and two variables (time and speed of ship B relative to ship A). We can solve these equations to find the time at which they will be 150 km apart.