Question

a ball thrown horizontally at 10 m/scrim thr too if a hill 50.0 m high. how far from the base of the cliff would the ball hit the ground

Answer 1

`\red{\frak{Given}}\begin{cases}\textsf{ A ball is thrown Horizontally at 10m/s from a hill.}\\\\\textsf{ The hill is 50m high. } \\\end{cases}`

To find :- How far does it land from the base of the cliff. (Range)

`\rule{100}1`

If a ball is thrown vertically from a height, then it's time of flight is given as;

`\sf\longrightarrow \boxed{\red{\sf Time_(of\ flight.) =\sqrt{(2H)/(g) } }} \\`

And the range i.e. distance between base of cliff to the point of landing is given as;

`\sf\longrightarrow \boxed{\red{\sf Range = u_x * Time_(of\ flight) }}\\`

where,

• H is the height of the cliff.
• g is acceleration due to gravity.
• 
  `\bf u_x` is horizontal velocity.

☯️
`\underline{\underline{\boldsymbol{ According \ to\ the\ question\ :- }}}`

`\sf\longrightarrow Range = \sqrt{(2H)/(g)} * u_x \\\\`

`\sf\longrightarrow Range = \sqrt{(2* 50\ m)/(10\ m/s^2)} * 10\ m/s \\\\`

`\sf\longrightarrow Range = √(10)* 10 \ m\\\\`

`\sf\longrightarrow Range = 3.16 * 10\ m \\\\`

`\sf\longrightarrow \underline{\boxed{\red{\mathfrak{ Range = 31.62\ m }}}} \quad \star \\\\`