a gun tilted upward at 30 degrees fires a bullet with a speed of 215 m/s. what is the bullets velocity parallel to the ground
To find the bullet's velocity parallel to the ground, we need to break down the initial velocity into its horizontal and vertical components.
The vertical component is the velocity in the upward or downward direction, and the horizontal component is the velocity parallel to the ground.
Given:
Initial velocity (v0) = 215 m/s
Angle of elevation (θ) = 30 degrees
To find the vertical component, we can use trigonometry. The vertical component can be calculated using the formula:
Vertical velocity (v_vertical) = v0 * sin(θ)
Let's substitute the given values:
v_vertical = 215 m/s * sin(30 degrees)
v_vertical = 215 m/s * 0.5
v_vertical = 107.5 m/s
The vertical component is 107.5 m/s.
Now, to find the horizontal component, we can use trigonometry again. The horizontal component can be calculated using the formula:
Horizontal velocity (v_horizontal) = v0 * cos(θ)
Let's substitute the given values:
v_horizontal = 215 m/s * cos(30 degrees)
v_horizontal = 215 m/s * (√3 / 2)
v_horizontal = 185.911 m/s
The horizontal component is approximately 185.911 m/s.
Therefore, the bullet's velocity parallel to the ground is approximately 185.911 m/s.