Question

A can sits on a vertical wooden fencepost 1.9 meters above the ground. Billy picks up a small rock, aims at an angle ϴ = 25⁰ above the horizontal and throws the rock, releasing it 1 m above the ground with an initial speed of v0 =10 m/s. Boom! He hits the can! How far away is the fencepost?

Answer 1

Given,

Height of the fencepost, h=1.9 m

Angle at which the rock was thrown, θ=25°

The height at which the rock was released, a=1 m

The initial speed of the rock, v₀=10 m/s

Referring to the diagram,

`\tan \theta=(h-a)/(d)`

On rearranging the above equation,

`d=(h-a)/(\tan \theta)`

On substituting the known values,

`d=(1.9-1)/(\tan 25^0)=1.93\text{ m}`

Therefore the fencepost is at a distance of 1.93 m