a boat moves with a velocity of 15m/s N in a river which flows with a velocity of 8.0m/s W. Calculate the boat's resultant velocity with respect to due north.
Need direction of flow of river.
1. Earth's first atmosphere was composed of mainly which of the following gases?
A. hydrogen and helium
B. carbon dioxide and oxygen
C. nitrogen and oxygen
D. carbon monoxide and o zone
2. During the Cambrian explosion that began the Paleozoic era, the many new forms of life that evolved
A. lived on land
B. were invertebrates that lived in the sea
C. were vertebrates covered with scales or fur
D. were single celled
3. which of the following occurred during the Mesozoic era?
A. the rise of reptiles
B. the rise of plants
C. the rise of invertebrates
D. the rise of mammals
it is going west
vector addition ... v^2 = 15^2 + 8.0^2 ... two significant figures
angle (west of north) ... tan(Θ) = 8 / 15
To calculate the boat's resultant velocity with respect to due north, we need to use vector addition. We can split the boat's velocity into two components: one along the north-south axis and the other along the east-west axis.
Given:
- Boat's velocity with respect to due north (V_boat_north) = 15 m/s
- River's velocity with respect to due west (V_river_west) = 8.0 m/s
Step 1: Determine the boat's velocity along the north-south axis.
Since the boat is moving strictly north with a velocity of 15 m/s, the magnitude of the boat's velocity component along the north-south axis (V_boat_north_south) is 15 m/s.
Step 2: Determine the boat's velocity along the east-west axis.
The river is flowing with a velocity of 8.0 m/s west. So, the magnitude of the river's velocity component along the east-west axis (V_river_east_west) is 8.0 m/s. However, since the boat is moving entirely north, there is no east-west component of its velocity. Thus, the magnitude of the boat's velocity component along the east-west axis (V_boat_east_west) is 0 m/s.
Step 3: Calculate the resultant velocity with respect to due north.
To find the boat's resultant velocity with respect to due north, we can use the Pythagorean theorem:
Resultant velocity (V_resultant) = √(V_boat_north_south^2 + V_boat_east_west^2)
Substituting the values:
V_resultant = √(15^2 + 0^2) = √(225 + 0) = √225 = 15 m/s
Therefore, the boat's resultant velocity with respect to due north is 15 m/s.