what is the range of an object moving on a y axis at 100m/s while also moving 50 m/s on an x axis
The range is unlimited, until it has gone once around the earth.
How long does it move at that velocity?
If y is vertical, ignore my previous answer. The y axis velocity will not remain 100 m/s if gravity is present.
To determine the range of an object moving on a y-axis at 100 m/s while also moving on an x-axis at 50 m/s, you need to know the time interval and the angle between the x and y axes.
The range of an object is the horizontal distance it travels. In this case, as the object is moving on both the x and y axes, you need to calculate the resultant velocity using vector addition. The resultant velocity will give you the magnitude and direction of the object's motion.
To find the resultant velocity, you can use the Pythagorean theorem. The magnitude of the resultant velocity (Vr) is given by:
Vr = √(Vx^2 + Vy^2)
Where Vx is the velocity in the x-direction (50 m/s) and Vy is the velocity in the y-direction (100 m/s).
Plugging in the values:
Vr = √(50^2 + 100^2) = √(2500 + 10000) = √12500 = 111.8 m/s (rounded to one decimal place)
The angle between the x and y axes will determine the direction of the object's motion. Let's assume the angle is θ.
Once you have the magnitude and direction of the resultant velocity, you can use trigonometry to find the x and y components of the velocity.
Vx = Vr * cos(θ)
Vy = Vr * sin(θ)
Since the object is moving at 50 m/s in the x-direction, Vx is already known.
To find Vy, you can rearrange the formulas above:
Vy = Vr * sin(θ) = 111.8 * sin(θ)
Now, if you know the time interval for which you want to calculate the range, you can use the equation:
Range = Vx * t
Where t is the time interval.
Therefore, to find the range on the y-axis, you need to know the angle between the x and y axes (θ), the magnitude of the resultant velocity (Vr), and the time interval (t) for which you want to calculate the range.