You are driving south on a highway at 24.0 m/s (approximately 54 mi/h) in a snowstorm. When you last stopped, you noticed that the snow was coming down vertically, but it is passing the windows of the moving car at an angle of 26.6° to the horizontal. Calculate the speed of the snowflakes relative to the car.
2.5
To calculate the speed of the snowflakes relative to the car, we can use vector addition.
Let's break down the velocities into horizontal (x) and vertical (y) components:
- Velocity of the car (Vc) in the x-direction (horizontal) = 24.0 m/s
- Velocity of the snowflakes (Vs) relative to the horizontal = Vsx (unknown component) + Vsy (vertical component)
The angle of 26.6° is the angle made by the snowflakes with the horizontal. We need to find the vertical component of the snowflakes' velocity.
Using trigonometry, we can find:
Vsy = Vs * sin(26.6°)
Now, we can calculate the speed of the snowflakes relative to the car:
Vs = √(Vsx^2 + Vsy^2)
Since we're given the speed of the car (Vc) as 24.0 m/s, we can substitute this value for Vsx in the equation.
Let's calculate the vertical component of the snowflakes' velocity first:
Vsy = Vs * sin(26.6°)
Vsy = Vs * 0.451
Now, we can calculate the speed of the snowflakes relative to the car:
Vs = √(Vsx^2 + Vsy^2)
Vs = √(24.0^2 + Vsy^2)
Substituting the calculated value of Vsy, we can simplify the equation:
Vs = √(24.0^2 + (Vs * 0.451)^2)
Squaring both sides of the equation:
Vs^2 = 24.0^2 + (Vs * 0.451)^2
Vs^2 = 576 + (0.203Vs)^2
Expanding and rearranging the equation:
Vs^2 - (0.203Vs)^2 = 576
Vs^2 - 0.041208Vs^2 = 576
0.958792Vs^2 = 576
Vs^2 = 602.5072
Taking the square root of both sides:
Vs = √602.5072
Vs ≈ 24.54 m/s
Therefore, the speed of the snowflakes relative to the car is approximately 24.54 m/s.
To calculate the speed of the snowflakes relative to the car, we can use vector addition.
The speed of the car is given as 24.0 m/s. We will consider this as the horizontal component of the velocity.
The angle between the direction of snowfall and the horizontal is given as 26.6°.
To find the vertical component of the snowflake's velocity, we can use trigonometry. The vertical component can be calculated as:
Vertical component = Speed of snowflakes * sin(angle)
So, the vertical component of the snowflake's velocity is:
Vertical component = Speed of snowflakes * sin(26.6°)
Now, we have the horizontal and vertical components of the snowflake's velocity. We can use these components to find the total velocity using the Pythagorean theorem:
Total velocity = sqrt((horizontal component)^2 + (vertical component)^2)
Since we want to find the speed of the snowflakes relative to the car, we need to subtract the speed of the car from the total velocity.
Therefore, the speed of the snowflakes relative to the car is:
Speed of snowflakes relative to car = Total velocity - Speed of the car
Now let's plug in the values and calculate:
Vertical component = Speed of snowflakes * sin(26.6°) = Speed of snowflakes * 0.445
Total velocity = sqrt((24.0 m/s)^2 + (Speed of snowflakes * 0.445)^2)
Speed of snowflakes relative to car = Total velocity - 24.0 m/s
To get the final result, you will need to substitute the value of the speed of snowflakes relative to the car into this equation and perform the calculations.