a child saw a skunk in a hole of a tree, standing 2.5m away. the child attempted to throw a pebble into the hole but missed with a speed of 11m/s. Angle of elevation is 75 degree, what was the Vfy of the pebble.
To find the vertical component of velocity (Vfy) of the pebble, we need to analyze the given information.
First, let's break down the initial velocity of the pebble into its horizontal and vertical components. We'll assume that the positive x-direction is towards the hole and the positive y-direction is upwards.
The initial velocity of the pebble can be split into its horizontal (Vfx) and vertical (Vfy) components using trigonometry. The given angle of elevation (θ) is 75 degrees.
Vfx = V * cos(θ)
Vfy = V * sin(θ)
Since the child missed the hole, the horizontal component of velocity remains constant at 11 m/s.
Vfx = 11 m/s
To calculate the vertical component of velocity (Vfy), we need to substitute the known angle of elevation (θ) and the known horizontal component of velocity (Vfx) into the equations.
Vfx = V * cos(θ)
11 m/s = V * cos(75°)
To isolate V and solve for it, divide both sides of the equation by cos(75°).
V = 11 m/s / cos(75°)
V ≈ 40.039 m/s (rounded to three decimal places)
Now that we have the initial velocity (V), we can calculate the vertical component of velocity (Vfy).
Vfy = V * sin(θ)
Vfy = 40.039 m/s * sin(75°)
Vfy ≈ 38.947 m/s (rounded to three decimal places)
Therefore, the vertical component of velocity (Vfy) of the pebble is approximately 38.947 m/s.