Question

A 0.30 kg football is thrown from a height of 2.5 m with an initial velocity of 25.0 m/s (34° above the horizontal axis). Assuming that there is no air resistance and that the ball lands on the ground, how far will the ball travel horizontally?

Answer 1

Given:

The mass of the football is,

`m=0.30\text{ kg}`

The initial height of the football is,

`h=2.5\text{ m}`

The initial velocity of the football is,

`u=25.0\text{ m/s}`

The angle with the horizontal is,

`\theta=34\degree`

To find:

how far will the ball travel horizontally

Step-by-step explanation:

The horizontal component of the initial velocity is,

`\begin{gathered} u_x=ucos\theta \\ =25.0* cos34\degree \\ =20.7\text{ m/s} \end{gathered}`

The vertical component of the initial velocity is,

`\begin{gathered} u_y=usin\theta \\ =25.0* sin34\degree \\ =13.9\text{ m/s} \end{gathered}`

Applying the equation of motion along the vertical direction we get,

`\begin{gathered} y=u_yt-(1)/(2)gt^2 \\ 1.8=13.9t-(1)/(2)*9.8* t^2 \\ 4.9t^2-13.9t+1.8=0 \\ t=(13.9\pm√((-13.9)^2-4*4.9*1.8))/(2*4.9) \\ t=(13.9\pm12.6)/(9.8) \\ t=2.70\text{ s, 0.13 s} \end{gathered}`

The horizontal distance covered by the football in this time is,

`\begin{gathered} d=u_xt \\ =20.7*2.70 \\ =55.9\text{ m} \\ or \\ d=20.7*0.13 \\ =2.69\text{ m} \end{gathered}`

Hence, the ball travels horizontally 55.9 m or 2.69 m.