A stone is thrown upwards with an initial velocity of 25m /s at an angle of 30 degree to the ground then explain why the horizontal component of the stone velocity at the start is 21.7m/s?
The horizontal component of the stone's velocity at the start is 21.7m/s because it is determined by the initial velocity and the angle of the throw. The horizontal component of the velocity is calculated using the equation vx = v * cos(angle), where v is the initial velocity and angle is the angle of the throw. In this case, vx = 25m/s * cos(30°) = 21.7m/s.
To explain why the horizontal component of the stone's velocity at the start is 21.7 m/s, we need to understand the concept of vector decomposition. When an object moves in two dimensions, such as in this case, its velocity can be broken down into two components: horizontal (x-axis) and vertical (y-axis).
In this scenario, the stone is thrown upwards at an angle of 30 degrees to the ground. The initial velocity of the stone, 25 m/s, consists of two components: the horizontal component (Vx) and the vertical component (Vy).
To find the horizontal component of the stone's velocity, we can use trigonometry. The horizontal component is determined by multiplying the magnitude of the total initial velocity (25 m/s) by the cosine of the angle (30 degrees):
Vx = 25 m/s * cos(30 degrees)
Vx = 25 m/s * 0.866 (rounded to three decimal places)
Vx ≈ 21.7 m/s
Therefore, the horizontal component of the stone's velocity at the start is approximately 21.7 m/s.
To understand why the horizontal component of the stone's velocity at the start is 21.7 m/s, we need to analyze the given information and apply the principles of trigonometry.
Given:
Initial velocity of the stone (V0) = 25 m/s
Angle of projection (θ) = 30 degrees
The velocity of a projectile can be divided into two components: the horizontal component (Vx) and the vertical component (Vy).
The horizontal component of the initial velocity (V0x) can be calculated using the equation:
V0x = V0 * cos(θ)
Where cos(θ) represents the cosine of the angle of projection.
Using this equation, we can calculate:
V0x = 25 m/s * cos(30°)
= 25 m/s * (√3 / 2)
≈ 21.7 m/s
Therefore, the horizontal component of the stone's velocity at the start is approximately 21.7 m/s. This component remains constant throughout the stone's motion, while the vertical component changes due to the effect of gravity.