Question

A footballer kicked a football with an initial speed of 25 m/s at an angle $\theta$ with the horizontal as shown in figure. Write down the equation of the projectile of the football when the ball is 7 $m$ (along x-axis) away from the footballer.

• A. $y=7tan\theta -\frac{49g}{1350co{s}^2\theta }$
• B. $y=tan\theta -\frac{9g}{1350cos\theta }$
• C. $y=7cot\theta -\frac{49g}{1350co{s}^2\theta }$
• D. $y=7tan\theta -\frac{41g}{1350cos2\theta }$

Answer 1

The correct option is A $y=7tan\theta -\frac{49g}{1350co{s}^2\theta }$

The equation of a projectile motion is a parabola , which is given by:

$y=x\tan \theta -\left(\frac{g}{2u^2{\cos }^2\theta }\right)x^2$

where, $x=$ horizontal distance travelled by object in time $t$

$y=$vertical distance travelled in time $t$

$\theta =$ angle of projection

$u=$ velocity of projection

Given: $u=25m/s,x=7m$

Hence, $y=7\tan \theta -\frac{7^{2}g}{2\times {25}^2{\cos }^2\theta }$

$y=7\tan \theta -\frac{49g}{1350{\cos }^2\theta }$