Answer:
39.26 m/s
Explanation:
Let the maximum height at which the object reaches is h.
Let the initial speed f the object is u.
velocity at height h/4 is 34 m/s
acceleration due to gravity = 9.8 m/s^2
For AB part
Use third equation of motion for AB part
here, initial velocity is v = 34 m/s
Final velocity at maximum height, v' = 0
Height = h - h/4 = 3h/4
[tex]v^{2}=u^{2}-2gh[/tex]
[tex]0^{2}=34^{2}-2\times 9.8 \times \frac {3h}{4}[/tex]
h = 78.64 m
For OA part
initial velocity = u
final velocity, v = 34 m/s
Height = h / 4 = 78.64 / 4 = 19.66 m
Use third equation of motion
[tex]v^{2}=u^{2}-2gh[/tex]
[tex]34^{2}=u^{2}-2\times 9.8 \times 19.66[/tex]
[tex]u^{2}=1541.336[/tex]
u = 39.26 m/s
