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A ball is thrown upward with an initial...

A ball is thrown upward with an initial velocity of `100ms^(-1)`. After how much time will it return? Draw velocity - time graph for the ball and find from the graph (i) the maximum height attained by the ball and (ii) height of the ball after 15 s. Take `g=10ms^(-2)`.

Text Solution

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Here, `u=100ms^(-1),g=-10ms^(-2)`
At highest point, `v=0`
As `v=u+g t therefore 0=100-10xxt`
`therefore` Time taken to reach highest point, `t=(100)/(10)=10s`
The ball will return to the ground at `t=20s`
Corresponding velocity - time graph of the ball is shown in
(i) Maximum height attained the ball = Area of `DeltaAOB`
`=(1)/(2)xx10xx100=500m`
(ii) Height attained after `15s` =
Area of `DeltaAOB+` Area of `DeltaBCD`
`=500+(1)/(2)(15-10)xx(-50)=500-125=375m`
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