A football is thrown upward at an angle of 30 degree with respect to the horizontal. To throw a 40 m pass what must be the initial speed of the ball? 

(Ans: 21 m s⁻¹)



Given:

Range of the projectile (football) = R =  40 m

Angle of projection = θ = 30°


To Find:

Initial Speed of the football = v = ?


Solution:


Using the formula of Range of projectile

R = `\frac {v_i^2}{g}`sin 2θ

or

`\v_i` = `\sqrt frac {Rg}{sin 2θ}`


by putting the corresponding values

`\v_i` = `\sqrt frac {40m ｘ 9.8 m s^{-2}}{sin 2x30°}`

`\v_i` = `\sqrt frac {392 m^2 s^{-2}}{sin 60°}`

`\v_i` = `\sqrt frac {392 m^2 s^{-2}}{0.866}`

`\v_i` = `\sqrt 452.66 m^2 s^{-2}`

`\v_i` = 21.3 m s⁻¹ -----------Ans.


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