A football is kicked with a velocity of 20 m/s at an angle of `45^0` with the horizontal. A. Find the time taken by the ball to strike the ground. find the maximum height it reaches. C. How far away from the kick downs it hit the ground? Take `g=10 m/s^2`.

Explanation

a. Take the origin at the point where theball is kicked, vertically upward as the Y-axis and the horizontl iln the plane of motion as the X-axis. The initial velocity has the components
`u_x=(20 m/s)cos45^0=10 sqrt2m/s`
and `u_y=(20 m/s)sin45^0=10 sqrt2 m/s`
When the ball reaches the ground, y=0.
Using `y=u_yt-1/2 gt^2,
`0=(10sqrt2m/s)t-1/2xx(10 m/s^2)xxt^2`
or, `t=2sqrt 2s=2.8 s.`
Thus, it takes 2.8s for the football to fall on the ground.
a. At the highest point `v_y ^2=u_y^2-2gy,`
`=0(10sqrt2m/s)^2-2xx(10 m/s^2)H`
`or H=10 m`
Thus, the maximum height reached is 10 m.
c. The horizontal distance travelled before falling to the ground is `x=u_xt`
`=(10 sqrt2 m/s)(2sqrt2s)=40m`