Physics 2000 JAMB Past Questions - Question 12: A stream is flowing at 0.75ms¹ and a boat heading perpendicular for the stream landed at the opposite bank at an angle 30. Calculate the velocity of the boat.

Correct Answer

E

Explanation

Sin30 =0.75/V V=1.5m/sTo calculate the velocity of the boat, we can use vector addition because the boat's motion has two components: one due to the stream's flow and the other perpendicular to it. A stream is flowing at 0.75ms¹ and a boat heading perpendicular for the stream landed at the opposite bank at an angle 30. Calculate the velocity of the boat.

Let's break down the boat's velocity into two components:

1. The velocity of the boat relative to the stream.
2. The velocity of the stream.

The velocity of the boat relative to the stream is the perpendicular component, and we can find it using trigonometry. We're given that the boat lands at an angle of 30 degrees with respect to the stream's direction. So, the component of the boat's velocity perpendicular to the stream is:

Velocity perpendicular to the stream = Boat's velocity * sin(30°)

Next, we need to consider the velocity of the stream, which is 0.75 m/s. This is the velocity of the stream in the direction of the boat's motion.

Now, to find the total velocity of the boat, we add the velocity of the boat relative to the stream (perpendicular component) to the velocity of the stream.

Total velocity of the boat = Velocity perpendicular to the stream + Velocity of the stream

Total velocity of the boat = (Boat's velocity * sin(30°)) + 0.75 m/s

Since you want to find the velocity of the boat, you'll need to know the value of the perpendicular component of the boat's velocity. If you provide that value or additional information, I can help you calculate the boat's velocity.
To calculate the velocity of the boat, we can use vector addition since the boat is moving perpendicular to the stream.

Given:
Stream velocity (v_stream) = 0.75 m/s
Angle between the boat's path and the stream (θ) = 30 degrees

Let's assume the velocity of the boat is v_boat.

The horizontal component of the boat's velocity (v_boat_horizontal) is equal to the stream velocity (v_stream) since the boat is heading perpendicular to the stream.

v_boat_horizontal = v_stream = 0.75 m/s

To find the vertical component of the boat's velocity (v_boat_vertical), we can use trigonometry. The vertical component can be calculated using the equation:

v_boat_vertical = v_boat * sin(θ)

Since the boat is heading perpendicular to the stream, the angle between the boat's path and the stream is 90 degrees. Therefore, sin(θ) = sin(90) = 1.

v_boat_vertical = v_boat * 1 = v_boat

Now, we can use the Pythagorean theorem to find the magnitude of the boat's velocity (v_boat):

v_boat = √(v_boat_horizontal² + v_boat_vertical²)
v_boat = √(0.75² + v_boat²)

Simplifying the equation:

v_boat² = v_boat² + 0.75²
0 = 0.75²

Since the equation does not have a solution, it means that the velocity of the boat cannot be determined based on the given information.