Projectile motions problems are some of the most important problems you will encounter in this course. Through this discussion, we will solve a projectile motion problem step by step
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 100m/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)?
parallel velocity=100cosine50
perpendicular =100sin50
To solve this projectile motion problem, we can break down the initial velocity into its components in the x-direction and y-direction using trigonometry.
Step 1: Understand the problem and identify given information:
- The angle of 50 degrees above the horizontal tells us the direction of the initial velocity.
- The initial speed of 100 m/s is the magnitude of the initial velocity.
Step 2: Calculate the initial velocity in the x-direction:
To find the initial velocity in the x-direction (Vx), we can use the formula: Vx = V * cos(theta), where V is the initial speed and theta is the launch angle.
Vx = 100 m/s * cos(50 degrees)
Vx ≈ 100 m/s * 0.64278760968
Vx ≈ 64.28 m/s
Therefore, the initial velocity parallel to the ground (in the x-direction) is approximately 64.28 m/s.
Step 3: Calculate the initial velocity in the y-direction:
To find the initial velocity in the y-direction (Vy), we also use the V * sin(theta) formula.
Vy = 100 m/s * sin(50 degrees)
Vy ≈ 100 m/s * 0.76604444311
Vy ≈ 76.60 m/s
Therefore, the initial velocity perpendicular to the ground (in the y-direction) is approximately 76.60 m/s.
In summary, the initial velocity of the projectile parallel to the ground (in the x-direction) is approximately 64.28 m/s, and the initial velocity perpendicular to the ground (in the y-direction) is approximately 76.60 m/s.