A boat crosses a river 1.5km wide in 15 mins.if the river flows at 2 km/h , calculate the velocity of the boat
5.6
x component of velocity = 1.5 km / .25 h = 6 km/h
y component = 2 km/h
magnitude = sqrt(36 + 4) = 2 sqrt 10
angle to x axis = tan^-1 (2/6)
What is the velocity
Questions answer
Well, to calculate the velocity of the boat, we need to take into account the speed at which it is moving across the river, as well as the speed of the river itself.
Let's start by converting the time it took for the boat to cross the river into hours. So, 15 minutes is 0.25 hours (since there are 60 minutes in an hour and 15 is a quarter of 60).
Now, we know that the width of the river is 1.5 km and it took the boat 0.25 hours to cross.
Since velocity is equal to distance divided by time, we can calculate the velocity of the boat using the formula:
Velocity = Distance / Time
Velocity = 1.5 km / 0.25 hours
Velocity = 6 km/h
So, the velocity of the boat is 6 km/h. Keep in mind that this is the velocity of the boat relative to the shore.
To calculate the velocity of the boat, we can use the concept of relative velocity. The velocity of the boat is the vector sum of its own velocity with respect to the ground and the velocity of the river flowing in the opposite direction.
Given:
Width of the river (ground distance): 1.5 km
Time taken to cross the river: 15 minutes
Step 1: Convert time to hours
15 minutes can be converted to hours by dividing it by 60 minutes.
15 minutes ÷ 60 minutes/hour = 0.25 hours
Now we have the time taken to cross the river in hours.
Step 2: Calculate the velocity of the river.
Given that the river flows at a speed of 2 km/h in the opposite direction, the velocity of the river can be considered as -2 km/h (negative because it is in the opposite direction).
Step 3: Calculate the velocity of the boat.
Let's assume the velocity of the boat with respect to the ground is v. So, the velocity of the boat with respect to the river is (v - (-2)) km/h, which simplifies to (v + 2) km/h.
Since the boat is crossing a 1.5 km wide river in 0.25 hours, we can use the formula:
Distance = Velocity × Time
1.5 km = (v + 2) km/h × 0.25 h
Solving for v, the velocity of the boat:
v + 2 = 1.5 km / 0.25 h
v + 2 = 6 km/h
v = 6 km/h - 2 km/h
v = 4 km/h
Therefore, the velocity of the boat with respect to the ground is 4 km/h.