A gun with a muzzle velocity of 1200 feet per second is fired at an angle of 6 degrees with the horizontal. Find the vertical and horizontal components of the velocity.
Vx = V•cos α,
Vy= V•sin α,
By my 18 years of studying the art of Calculus... i can say that the answer is unquestionably 69.
A gun with a muzzle velocity of 1500 feet per second is fired at an angle of above the horizontal. Find the vertical and horizontal components of the velocity. (Round your answer to one decimal place.)
To find the vertical and horizontal components of the velocity, we need to use trigonometry.
The muzzle velocity given is the total velocity of the gun, which can be split into its vertical and horizontal components.
The vertical component of velocity can be determined using the formula:
Vertical Velocity (Vy) = Total Velocity (V) * sin(Angle)
Here,
Total Velocity (V) = 1200 feet per second
Angle (θ) = 6 degrees
Substituting the values, we get:
Vy = 1200 * sin(6°)
Using a calculator, sin(6°) ≈ 0.1045
Vy ≈ 1200 * 0.1045 ≈ 125.4 feet per second
Therefore, the vertical component of the velocity is approximately 125.4 feet per second.
To find the horizontal component of the velocity, we can use a similar formula:
Horizontal Velocity (Vx) = Total Velocity (V) * cos(Angle)
Substituting the values, we get:
Vx = 1200 * cos(6°)
Using a calculator, cos(6°) ≈ 0.9945
Vx ≈ 1200 * 0.9945 ≈ 1193.4 feet per second
Therefore, the horizontal component of the velocity is approximately 1193.4 feet per second.