Answer:
All the balls hit the ground with same velocity.
Explanation:
Let the speed of throwing be u and height of building be h.
Ball A is launched 45 degrees above the horizontal
Initial vertical speed = usin45
Vertical acceleration = -g
Height = -h
Substituting in v² = u² +2as
v² = (usin45)² -2 x g x (-h)
v² = 0.5u² +2 x g x h
Final vertical speed² = 0.5u² +2 x g x h
Initial horizontal speed = final horizontal speed = ucos45
Final horizontal speed² = 0.5u²
Magnitude of final velocity
[tex]v=\sqrt{0.5u^2+2gh+0.5u^2}=\sqrt{u^2+2gh}[/tex]
Ball C is launched horizontally
Initial vertical speed = 0
Vertical acceleration = -g
Height = -h
Substituting in v² = 0² +2as
v² = 0² -2 x g x (-h)
v² = 2 x g x h
Final vertical speed² = 2 x g x h
Initial horizontal speed = final horizontal speed = u
Final horizontal speed² =u²
Magnitude of final velocity
[tex]v=\sqrt{2gh+u^2}=\sqrt{u^2+2gh}[/tex]
Ball B is launched 45 degrees below the horizontal
Initial vertical speed = usin45
Vertical acceleration = g
Height = h
Substituting in v² = u² +2as
v² = (usin45)² +2 x g x h
v² = 0.5u² +2 x g x h
Final vertical speed² = 0.5u² +2 x g x h
Initial horizontal speed = final horizontal speed = ucos45
Final horizontal speed² = 0.5u²
Magnitude of final velocity
[tex]v=\sqrt{0.5u^2+2gh+0.5u^2}=\sqrt{u^2+2gh}[/tex]
All the magnitudes are same so all the balls hit the ground with same velocity.
The ball C which was launched horizontally will hit the ground fastest.
With respect to angle of projection above the horizontal, the time of motion each ball is calculated as follows;
[tex]T = \frac{u sin\theta }{g}[/tex]
where;
When θ is 45 degrees above the horizontal;
[tex]T = \frac{u \times sin(45)}{9.8}\\\\ T = 0.072u[/tex]
When θ is 45 degrees below the horizontal = 135 degrees above the horizontal
[tex]T = \frac{ u \times sin(135)}{9.8} \\\\T = 0.072 \ s[/tex]
When launched horizontally, θ = 90 degrees above the horizontal
[tex]T = \frac{u \times sin(90)}{9.8} \\\\T = 0.1 u[/tex]
Thus, the ball C which was launched horizontally will hit the ground fastest.
Learn more about time of motion here: https://brainly.com/question/2364404
