A boat propelled so as to travel with a speed of 0.5m/s in still water, moves directly (in a straight line) across a river that is 60m wide. The river flows with a speed of 0.30m/s. How long in seconds does it take the boat to cross the river?
RV =√(0.50)²-(0.30)²
=0.4m/s
Data
T=?s
V=0.4m/s
D=60m
V=d/t
T=d/v
T=60/0.4 =150
T=150seconds
To find the time it takes for the boat to cross the river, we can use the concept of relative velocity.
Step 1: Determine the velocity of the boat relative to the ground.
The boat's speed in still water is given as 0.5 m/s. Since there is no information given about the direction of the river's flow, we can assume it is perpendicular to the direction of the boat's motion. Therefore, the boat's velocity relative to the ground remains 0.5 m/s.
Step 2: Determine the velocity of the boat relative to the river.
The boat's velocity relative to the river can be calculated by subtracting the velocity of the river from the boat's velocity relative to the ground.
Velocity of the boat relative to the river = Velocity of the boat relative to the ground - Velocity of the river
= 0.5 m/s - 0.3 m/s
= 0.2 m/s
Step 3: Calculate the time it takes for the boat to cross the river.
The time it takes for the boat to cross the river can be found by dividing the width of the river by the boat's velocity relative to the river.
Time = Distance / Velocity
= 60 m / 0.2 m/s
= 300 seconds
Therefore, it takes the boat 300 seconds to cross the river.
To find out how long it takes for the boat to cross the river, we can use the concept of relative velocity.
The boat is traveling at a speed of 0.5 m/s in still water, and the river is flowing with a speed of 0.30 m/s.
When the boat is crossing the river, it is actually moving in the direction perpendicular to the flow of the river. The effective speed of the boat in the direction across the river can be calculated using the Pythagorean theorem.
Let's denote the effective speed of the boat across the river as V_eff.
Using the Pythagorean theorem, we have:
V_eff^2 = (V_boat)^2 + (V_river)^2
V_eff^2 = (0.5 m/s)^2 + (0.30 m/s)^2
V_eff^2 = 0.25 m^2/s^2 + 0.09 m^2/s^2
V_eff^2 = 0.34 m^2/s^2
Taking the square root of both sides, we get:
V_eff ≈ 0.583 m/s
Now, let's calculate the time it takes for the boat to cross the river.
The distance across the river is given as 60m. We can use the formula: time = distance / speed.
time = distance across the river / effective speed of the boat
time = 60m / 0.583 m/s
time ≈ 102.94 seconds
Therefore, it takes approximately 102.94 seconds for the boat to cross the river.
tanA = 0.3/0.5 = 0.6
A = 31o
D = 60/cos31 = 70 m.
V = 70/cos31 = 0.583 m/s
D = V*t = 70 m.
0.583*t = 70
t = 120.1 s.