Answer:
The horizontal reaction force is 230.3 N.
Explanation:
Given that,
Length l= 14.0 m
Weight of ladder F = 490 N
Angle = 65°
Weight of firefighter F'= 850 N
Height l'= 4.10 m
Suppose horizontal force magnitude N direction vertical force magnitude N direction
We need to calculate the horizontal reaction force
Horizontal reaction force = normal reaction from wall
Vertical reaction force = weight of ladder +weight of man
[tex]F=490+850[/tex]
[tex]F=1340\ N[/tex]
We need to calculate the moment about bottom is zero
[tex]N\times l\sin\theta=F\times\dfrac{l}{2}\cos\theta+F'\times l'\cos\theta[/tex]
Put the value in the equation
[tex]N\times14\sin(65)=490\times7\cos(65)+850\times4.10\cos(65)[/tex]
[tex]N=\dfrac{490\times7\cot(65)+850\times4.10\cot(65)}{14}[/tex]
[tex]N=230.3\ N[/tex]
Hence, The horizontal reaction force is 230.3 N.
