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A body is thrown horizontally from the t...

A body is thrown horizontally from the top of a tower and strikes the ground after three seconds at an angle of ` 45^(@)` ,with the horizontal . Then find ,
(i) The height of the lower
(ii) The speed of projection of the body

Text Solution

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(i) Let H be the height of the lower
The time of filight ` T_(t) = sqrt((2H)/g) = 3s`
` Rightarrow H = ( g xx (3)^(2))/2`
` = ( 9.8 xx 9)/2`
44.1 m.
(ii) Let the speed of projection be `v_(0)` , then for horizontal projection.
` v_(x) = v_(0)`
` v_(y) = -gt`
At ` t = T_(i) = 3s`
` v_(y) = - 9.8 xx 3`
` = 29. 4 "m s"^(-1)`
The angle which the final velocity makes with the horizontal = `theta = 45^(@)`
` Rightarrow - tan 45^(@) = ( -v_(y))/(v_(x))`
` Rightarrow v_(y) = v_(x)`
So, ` v_(x) = 29. 4 ms^(-1)`
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