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A ball is thrown from the origin in the ...

A ball is thrown from the origin in the x-y plane with velocity `28.28m//s` at an angle of `45^(@)` with x-axis.At the same instant a trolley also starts moving with uniform velocity of `10m//s` along the positive x-axis . Initially , the trolley is located at 38m from the origin. Determine the time at which the ball hits the trolley.

Text Solution

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Let t be the instant at which the ball hits rear face AB of the trolley.
Then `(v_(0)cos 45^(@)-u_(0))t=38`
(or) `t=38/(v_(0)cos 45^(@)-u_(0))=38/(28.28cos 45^(@)-10)=3.8s`
At `t=3.8s` then y-coordinate of the ball is

`y=(v_(0)sin 45^(@))t-1/2"gt"^(2)=20t-5t^(2)`
(or) `y=20(3.8)-5(3.8)^(2)=3.8m`
Since `3.8mgt2m`, therefore, the ball cannot hit the reat of face of the trolley. Now e assume that the ball hits the top face BC of the torlley, and let t bet aht instant. Then
`=2=20t.-5t^(-2)` or `t^(.2)-4t.+0.4=0,t^(.)=3.9s`
Let d be the disance from the point B at which the ball hits trolley. Then
`d=(v_(0)cos 45^(@)-u_(0))(t.-t)=(20-10)(3.9-3.8)=1M`
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