Assume a projectile is launched from ground height over a flat plane, at an angle of 50 degrees above the horizontal with an initial speed of 100 m/s.
What is the initial velocity of the projectile parallel to the ground (in the x direction) and perpendicular to the ground (in the y direction)? Show all of your work.
Vo = 100m/s[50o]
Xo = 100*cos50
Yo = 100*sin50
To determine the initial velocity of the projectile in the x-direction and y-direction, we can use the given information.
Given:
Initial launch angle (θ) = 50 degrees
Initial speed (V₀) = 100 m/s
To find the initial velocity in the x-direction (V₀x), we need to calculate the horizontal component of the velocity. The horizontal component can be found using the formula:
V₀x = V₀ * cos(θ)
where cos(θ) represents the cosine of the angle θ.
Plugging in the values:
V₀x = 100 m/s * cos(50 degrees)
Using a scientific calculator, calculate cos(50 degrees):
V₀x = 100 m/s * 0.6428
V₀x = 64.28 m/s
Therefore, the initial velocity of the projectile in the x-direction is 64.28 m/s.
To find the initial velocity in the y-direction (V₀y), we need to calculate the vertical component of the velocity. The vertical component can be found using the formula:
V₀y = V₀ * sin(θ)
where sin(θ) represents the sine of the angle θ.
Plugging in the values:
V₀y = 100 m/s * sin(50 degrees)
Using a scientific calculator, calculate sin(50 degrees):
V₀y = 100 m/s * 0.7660
V₀y = 76.60 m/s
Therefore, the initial velocity of the projectile in the y-direction is 76.60 m/s.
In summary:
Initial velocity of the projectile in the x-direction (V₀x) = 64.28 m/s
Initial velocity of the projectile in the y-direction (V₀y) = 76.60 m/s