A cannon on top of a 119m tall cliff fires acannonball at a boat. The cannonball

Question

A cannon on top of a 119m tall cliff fires acannonball at a boat. The cannonball has an initialvelocity of 118m/s at 62degrees above horizontal. Ignore airresistance. how long does it take the cannonball to land in the water nearthe boat, and how far away does the cannonball land from thecannon. Also, what angle (below horizontal) is the cannonballtraveling when it hits the water. A cannon on top of a 119m tall cliff fires acannonball at a boat. The cannonball has an initialvelocity of 118m/s at 62degrees above horizontal. Ignore airresistance. how long does it take the cannonball to land in the water nearthe boat, and how far away does the cannonball land from thecannon. Also, what angle (below horizontal) is the cannonballtraveling when it hits the water.

Explanation / Answer

Height h = 119 m Initial velocity v = 118 m / s angle = 62 degrees In vertical direction : - -------------------- Initial velocity u = v sin                         = 104.18 m / s Displacement S = h = 119 m Accleration a= g = 9.8 m / s ^ 2 from the relation S= ut + (1/2 ) at ^2                119 = 104.18 t + 9.8 t ^ 2        9.8 t ^ 2 + 104.18 t-119 = 0 t = { -104.18 ± [ 104.18^2 -(4*9.8*-119) ] } /2(9.8 ) = { -104.18 ± 124.57 } / 19.6 = 1.04 s    Since negative time isnot exist (b). Horizontal velocity V = v cos = 55.39 m /s Required distance = V t                            57.62 m

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