A girl riding a bicycle with a speed of 5m/s towards northdirection , observes rain falling vertically down. If she increases her speed to 10m/s , rain appears to meet her at 45degree tp the vertical .what is the speed of rain ?
To solve this problem, we need to understand the concept of relative motion. Let's break it down step by step:
Step 1: Analyze the initial scenario
In the initial scenario, the girl is riding a bicycle with a speed of 5 m/s toward the north direction. The rain is falling vertically down. We need to determine the speed of rain in this situation.
Since the girl is moving towards the north and the rain is falling vertically, the rain appears to come towards the girl at a certain angle due to her motion.
Step 2: Analyze the scenario with increased speed
In the second scenario, the girl increases her speed to 10 m/s. Now, the rain appears to meet her at an angle of 45 degrees to the vertical.
Step 3: Determine the speed of rain
To find the speed of rain, we need to consider the concept of relative motion. The apparent angle at which the rain meets the girl is equal to the angle between the velocity vector of the girl and the velocity vector of the rain.
In the initial scenario, the vertical component of the girl's velocity is zero, as she is moving only in the north direction. So, the angle between the velocity vectors of the girl and the rain is equal to the angle between the rain's velocity vector and the vertical direction.
In the second scenario, the rain appears to meet the girl at an angle of 45 degrees to the vertical. This means that the angle between the rain's velocity vector and the vertical direction is also 45 degrees.
By using trigonometry, we can find the speed of rain. The vertical component of rain's velocity is given by:
Vertical component of rain's velocity = Speed of rain * sin(45 degrees)
Since the vertical component of the girl's velocity is zero, the vertical component of the rain's velocity should be equal to the vertical component of the girl's velocity in the second scenario.
Vertical component of rain's velocity = Vertical component of girl's velocity in the second scenario
Finally, we can use the given information to solve for the speed of rain:
Vertical component of rain's velocity = Vertical component of girl's velocity in the second scenario
Speed of rain * sin(45 degrees) = 10 m/s
Solving for the speed of rain:
Speed of rain = 10 m/s / sin(45 degrees)
Calculating this value will give you the speed of rain.