A projectile is launched from the origin with a speed of 2 ms−1 at the angle of 60∘ from the horizontal. Assume that ground to be flat and plane of trajectory to be x-y plane with x-axis along horizontal. The radial and tangential components of its velocity at its highest point are given by.
A projectile is launched from the origin with a speed of 2 ms−1 at the angle of 60∘ from the horizontal. Assume that ground to be flat and plane of trajectory to be x-y plane with x-axis along horizontal. The radial and tangential components of its velocity at its highest point are given by.
To find the radial and tangential components of the velocity at the highest point of the projectile's trajectory, we first need to understand the motion of the projectile and its trajectory.
The motion of a projectile can be divided into two independent components: horizontal and vertical. The horizontal motion is constant and unaffected by gravity, while the vertical motion is affected by gravity and follows a parabolic trajectory.
Given that the projectile is launched from the origin (0,0) with a speed of 2 m/s at an angle of 60 degrees from the horizontal, we can break down the initial velocity into its horizontal and vertical components.
Horizontal component:
The initial horizontal velocity (Vx) remains constant throughout the trajectory. It can be found using the equation:
Vx = V * cosθ
where V is the initial speed (2 m/s) and θ is the launch angle (60 degrees).
Vx = 2 m/s * cos(60 degrees)
Vx = 1 m/s
Vertical component:
The initial vertical velocity (Vy) can be found using the equation:
Vy = V * sinθ
where V is the initial speed (2 m/s) and θ is the launch angle (60 degrees).
Vy = 2 m/s * sin(60 degrees)
Vy = √3 m/s
At the highest point of the trajectory, the projectile's vertical velocity becomes zero, and gravity is acting in the opposite direction. Therefore, we can find the radial component of the velocity at the highest point by taking the negative of the horizontal component:
Vradial = -Vx
Vradial = -1 m/s
The tangential component of the velocity at the highest point is equal to the vertical component:
Vtangential = Vy
Vtangential = √3 m/s
Therefore, the radial component of velocity at the highest point is -1 m/s, and the tangential component of velocity at the highest point is √3 m/s.