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

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