Projectile Motion: Position and Velocity Calculation
Projectile motion is a fascinating concept in physics that involves the motion of objects in two dimensions under the influence of gravity. When a ball is kicked or thrown into the air at an angle, we can analyze its position and velocity at different time intervals to understand its trajectory.
Position Calculation:
For the horizontal direction, we use the equation: X = Vx*t, where Vx = V * cos(θ). Substituting the values, we get X = 20 * cos(30) * 1.5.
For the vertical direction, we use the equation: Y = Vy*t - 0.5gt^2, where Vy = V * sin(θ) and g is the acceleration due to gravity. Substituting the values, we get Y = 20 * sin(30) * 1.5 - 0.5 * 9.8 * 1.5^2.
Velocity Calculation:
For the horizontal component of velocity, there is no acceleration, so Vx remains constant at 20 * cos(30) m/s.
For the vertical component of velocity at 1.5 seconds, we calculate Vy(t) = Vy - g * t. Substituting the values, we get Vy(1.5) = 20 * sin(30) - 9.8 * 1.5 m/s.
Therefore, the position of the ball after 1.5 seconds is X = 17.32 m and Y = 8.78 m, while the velocity components are Vx = 17.32 m/s and Vy(1.5) = 5.9 m/s.