Answer:
The final speed is <em>30.37 m/s</em> for the three directions.
Explanation:
Given the initial speed, v₀ = 14.7 m/s and the height of the building as 36.0 m (neglecting air resistance and height of slingshot), we apply the principle of Conversation of Mechanical Energy:
E = Kinetic Energy (k.E) + Potential Energy (P.E)
K.E = 0.5mv²
P.E = mgh
∴ <em>0.5mv₀² + mgh₀ = 0.5mv₁² + mgh₁</em>
Since the final height (h₁) is zero and <em>m</em> is a common term, then we can re-write the above equation as:
<em>0.5v₀² + gh₀ = 0.5v₁² + 0</em>
<em>0.5v₁² - 0.5v₀² = gh₀</em>
<em>0.5(v₁² - v₀²) = gh₀</em>
<em>v₁² = v₀² + 2gh₀</em>
Fitting in the given terms, we can calculate the final speed
v₁² = (14.7)² + (2)(9.81)(36.0)
= 216.09 + 706.32 = 922.41
v₁ = √922.41 = 30.37 m/s.
The speed at which the pebble hits the ground remains the same because kinetic energy depends on the speed of the object and not the direction to which the object is thrown.
