A stone is thrown upwards with an initial velocity of 25m/s at an angle of 30 degree to the ground then find what will the stone horizontal velocity be just before it lands
on the ground
The horizontal velocity of the stone just before it lands on the ground will be the same as its initial horizontal velocity, which is 21.2 m/s. This can be calculated using the equation:
vx = v0 * cos(θ)
where vx is the horizontal velocity, v0 is the initial velocity, and θ is the angle of the throw. In this case, vx = 25 * cos(30) = 21.2 m/s.
To find the horizontal velocity of the stone just before it lands, we need to separate the initial velocity into its horizontal and vertical components.
Given:
Initial velocity (v₀) = 25 m/s
Launch angle (θ) = 30 degrees
The horizontal velocity (vₓ) remains constant throughout the motion. Therefore, the horizontal velocity just before the stone lands will be the same as the initial horizontal velocity.
To find the horizontal velocity, we can use the equation:
vₓ = v₀ * cos(θ)
First, convert the angle from degrees to radians:
θ_rad = θ * pi/180
θ_rad = 30 * pi/180
θ_rad = pi/6
Now, we can calculate the horizontal velocity:
vₓ = 25 * cos(pi/6)
vₓ ≈ 25 * 0.866
vₓ ≈ 21.65 m/s
Therefore, the horizontal velocity of the stone just before it lands will be approximately 21.65 m/s.
To find the horizontal velocity of the stone just before it lands, we need to understand the horizontal and vertical components of the stone's motion.
The horizontal component of the stone's velocity will remain constant throughout its motion because there is no acceleration acting in the horizontal direction. Therefore, the horizontal velocity at any point in its trajectory will be the same as its initial horizontal velocity.
Given that the initial velocity (V₀) of the stone is 25 m/s, and it is thrown at an angle of 30 degrees to the ground, we can determine the horizontal component (Vx) using trigonometry.
Vx = V₀ * cosθ
Here, θ is the angle of 30 degrees.
Vx = 25 m/s * cos(30°)
= 25 m/s * (√3/2)
≈ 25 m/s * 0.866
≈ 21.65 m/s
Therefore, the stone's horizontal velocity just before it lands will be approximately 21.65 m/s.