Answer:
The final velocity is 5.24 m/s
The initial speed is 65.5 m/s
Explanation:
Horizontal Motion
When an object is launched horizontally with an initial speed v from a height h, it describes a curved path ruled exclusively by gravity until it eventually hits the ground.
The horizontal component of the velocity is always constant because no acceleration acts in that direction, thus:
[tex]v_x=v_o[/tex]
The vertical component of the velocity changes in time t because gravity makes the object fall at increasing speed given by:
[tex]v_y=g.t[/tex]
The maximum horizontal distance traveled by the object can be calculated as follows:
[tex]\displaystyle d=v\cdot\sqrt{\frac {2h}{g}}[/tex]
Another useful formula allows us to calculate the distance traveled by the object in terms of time t:
[tex]\displaystyle y=\frac{g.t^2}{2}[/tex]
a.
The time taken for the arrow to reach the ground can be calculated by solving the above equation for t:
[tex]\displaystyle t=\sqrt{\frac{2y}{g}}[/tex]
Since y=1.40 m:
[tex]\displaystyle t=\sqrt{0.2857}[/tex]
t = 0.53 s
The final vertical speed is:
[tex]v_y=9.8.(0.53)=5.24\ m/s[/tex]
The final velocity is 5.24 m/s
b)
The initial speed can be calculated by solving the following equation for v:
[tex]\displaystyle d=v\cdot\sqrt{\frac {2h}{g}}[/tex]
[tex]\displaystyle v=d\cdot\sqrt{\frac {g}{2h}}[/tex]
[tex]\displaystyle v=35\cdot\sqrt{\frac {9.8}{2(1.40)}}[/tex]
v = 65.5 m/s
The initial speed is 65.5 m/s
