a cannon ball is shot from a 100 m high cliff with an inital velocity of 24m/s and at an angle of 32 degrees. what is the overall final velocity of the cannonball?
WEll,the kinetic energy of the ball at the end must equal the initial KE added to the initialpe
1/2 m vf^2=1/2 m vi^2+mg*100
solve for Vf
To find the overall final velocity of the cannonball, we need to break down the initial velocity into its horizontal and vertical components. The horizontal component represents the velocity in the x-direction, while the vertical component represents the velocity in the y-direction.
Given:
Initial velocity (v₀) = 24 m/s
Angle (θ) = 32 degrees
First, we can find the vertical component of the initial velocity (v₀y):
v₀y = v₀ * sin(θ)
= 24 * sin(32°)
Next, we can find the horizontal component of the initial velocity (v₀x):
v₀x = v₀ * cos(θ)
= 24 * cos(32°)
Now, we can analyze the vertical motion of the cannonball. Since the only force acting on it in the vertical direction is gravity, we can use the equations of motion to determine the final vertical velocity (vf_y). The final vertical velocity can be found using the equation:
vf_y² = v₀y² + 2 * g * Δy
Where:
g is the acceleration due to gravity (approximately 9.8 m/s²)
Δy is the change in vertical displacement, which is equal to the height of the cliff (100 m in this case).
Simplifying the equation, we get:
vf_y = √(v₀y² + 2 * g * Δy)
Now, let's calculate the values:
v₀y = 24 * sin(32°)
v₀x = 24 * cos(32°)
g = 9.8 m/s²
Δy = 100 m
Substituting the values:
vf_y = √(v₀y² + 2 * g * Δy)
Finally, to find the overall final velocity of the cannonball, we need to combine the horizontal and vertical components. The overall final velocity (vf) can be found using the Pythagorean theorem:
vf = √(vf_x² + vf_y²)
Since we already have the values for vf_y and vf_x, we can substitute these values into the equation to find the overall final velocity.
I'll calculate the values and provide you with the final answer.