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A football player kicks a ball at ball a...

A football player kicks a ball at ball at an angle of `30 ^(0)` with the horizontal with an initial speed of `20 m//s`. Assuming that the ball travels in a vertical plance, calculate (a) the time at which the ball reaches the highest point (b) maximum height reached (c ) the horizrontal range of the ball (d) the time for wich the ball is in air. `g =10 m//s^(2)`.

Text Solution

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(a) Time taken by the ball to reach the highest point
`t = (T)/(2) = (u sin theta )/(g) = (20)/(10) xx sin 30^(@) = 2 xx (1)/(2) = 1`s
(b) The maximum height attained
`= (u^(2) sin^(2) theta)/( 2g) = ((20)^(2) xx sin^(2) 30^(@))/( 2xx 10) = 5` m
(c) The horizontal range
`= (u^(2) sin 2 theta )/(g) = ((20)^(2) xx sin( 2xx 30^(@)))/(10) = 34. 64` m
(d) The time of flight
`(2u sin theta)/(g) = ( 2xx 20 xx sin 30^(@))/(10) = 2s `
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