A projectile fired at 30 degrees with a velocity if 15 m/s would have an
x-velocity component of????m/s and a
y-velocity component of????m/s.
Please help.. thank you
x: 15 cos30
y: 15 sin30
To find the x-velocity component and y-velocity component of a projectile fired at an angle, we can use trigonometry and the given information about the angle and velocity.
First, let's define the given information:
Angle of projection: 30 degrees
Velocity of projectile: 15 m/s
To find the x-velocity component, we need to calculate the horizontal velocity. This can be done using the formula:
Horizontal velocity (Vx) = Velocity (V) * cos(angle)
Plugging in the given values:
V = 15 m/s
angle = 30 degrees
Vx = 15 m/s * cos(30 degrees)
Using the cosine of 30 degrees (which is √3/2), we have:
Vx = 15 m/s * (√3/2)
Calculating this, we find:
Vx ≈ 15 m/s * 0.866 ≈ 12.99 m/s
Therefore, the x-velocity component is approximately 12.99 m/s.
To find the y-velocity component, we need to calculate the vertical velocity. This can be done using the formula:
Vertical velocity (Vy) = Velocity (V) * sin(angle)
Plugging in the given values:
V = 15 m/s
angle = 30 degrees
Vy = 15 m/s * sin(30 degrees)
Using the sine of 30 degrees (which is 1/2), we have:
Vy = 15 m/s * (1/2)
Calculating this, we find:
Vy = 15 m/s * 0.5 = 7.5 m/s
Therefore, the y-velocity component is 7.5 m/s.
In summary, the projectile fired at 30 degrees with a velocity of 15 m/s has an x-velocity component of approximately 12.99 m/s and a y-velocity component of 7.5 m/s.