calculate the velocity of 10 meters per second with an angle of 30 degrees
Was there a picture given? I don't know if I can answer the question without a picture.
To calculate the velocity of an object given its magnitude (10 meters per second) and angle (30 degrees), you will need to break down the velocity into its horizontal and vertical components.
First, let's find the horizontal component of the velocity. To do this, we use the formula:
horizontal velocity = velocity * cos(angle)
In this case, the horizontal velocity is equal to 10 meters per second multiplied by the cosine of 30 degrees:
horizontal velocity = 10 m/s * cos(30°)
Using a scientific calculator or online calculator that supports trigonometric functions, calculate the cosine of 30 degrees:
cos(30°) ≈ 0.866
Now substitute the value we obtained for the cosine of 30 degrees into the equation:
horizontal velocity = 10 m/s * 0.866 ≈ 8.66 m/s
So, the horizontal component of the velocity is approximately 8.66 meters per second.
Next, let's find the vertical component of the velocity. To do this, we use the formula:
vertical velocity = velocity * sin(angle)
In this case, the vertical velocity is equal to 10 meters per second multiplied by the sine of 30 degrees:
vertical velocity = 10 m/s * sin(30°)
Using the same scientific calculator or online calculator, calculate the sine of 30 degrees:
sin(30°) ≈ 0.5
Now substitute the value we obtained for the sine of 30 degrees into the equation:
vertical velocity = 10 m/s * 0.5 = 5 m/s
Therefore, the vertical component of the velocity is 5 meters per second.
To find the overall velocity, we can use the Pythagorean theorem:
velocity = √(horizontal velocity^2 + vertical velocity^2)
Substitute the values we obtained:
velocity = √(8.66^2 + 5^2) ≈ √(75 + 25) ≈ √100 ≈ 10 m/s
Hence, the velocity of the object with a magnitude of 10 meters per second and an angle of 30 degrees is approximately 10 meters per second.