Answer:
27.32 m
Step-by-step explanation:
We are given that
Height of window from the ground=18 m
Height of rock form the ground=2 m
Speed of thrown rock=30 m/s
We have to find the horizontal distance from the window from which rock was release.
Difference between window and rock=18-2=16 m
Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s
Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]
If the rock is reached to maximum height
Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]
Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]
Distance between window and maximum height at which rock reached=18.9731-16=2.973 m
Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]
Time to be at 16 m=1.96775-0.77893=1.189 s
Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]
Hence, horizontal distance of rock from the window from which rock was released=27.32 m
