Danny sails a boat downstream. The wind pushes the boat along at 21 km/hr. The current runs downstream at 15 km/hr. What is the actual velocity of the boat
36 km/hr, downstream
To find the actual velocity of the boat, we need to calculate the resultant velocity by considering the velocity of the wind and the velocity of the current.
Step 1: Write down the given velocities:
- Velocity of the wind (W) = 21 km/hr (downstream)
- Velocity of the current (C) = 15 km/hr (downstream)
Step 2: Add the velocities vectorially to find the resultant velocity:
Resultant velocity (R) = W + C
Step 3: Add the magnitudes of the velocities:
Magnitude of W = 21 km/hr
Magnitude of C = 15 km/hr
Step 4: Combine the magnitudes:
Magnitude of R = Magnitude of W + Magnitude of C
= 21 km/hr + 15 km/hr
= 36 km/hr
Step 5: Determine the direction of the resultant velocity:
Since both the wind and the current were going downstream, the resultant velocity will also be downstream.
Therefore, the actual velocity of the boat is 36 km/hr downstream.
To find the actual velocity of the boat, we need to consider the velocities of both the wind and the current.
When sailing downstream, the boat uses the velocity of the current to its advantage, increasing its overall speed. In this case, the current runs downstream at 15 km/hr, so the boat's velocity is increased by this amount.
However, the wind is also pushing the boat along at a speed of 21 km/hr. Since both the wind and the current are acting in the same direction, we can simply sum up their velocities to find the actual velocity of the boat.
Therefore, to find the actual velocity of the boat, we add the velocity of the wind (21 km/hr) to the velocity of the current (15 km/hr):
Actual velocity = 21 km/hr + 15 km/hr
Actual velocity = 36 km/hr
Hence, the actual velocity of the boat is 36 km/hr.
Vb + Vc = 21 km/h,
Vc = 15 km/h,
Vb + 15 = 21,
Vb = 21 - 15 = 6 km/h = Velocity of boat.