Answer:
Weight = 734.46 N
Explanation:
Given:
Initial height of the pole-vaulter is, [tex]h_i=5.31\ m[/tex]
Final height of the pole-vaulter is, [tex]h_f=0\ m[/tex]
Change in the vaulter's potential energy is, [tex]\Delta U=-3900\ J[/tex]
We know that, change in potential energy is given as:
[tex]\Delta U=mg(h_f-h_i)[/tex]
Where, 'm' is the mass of the object, 'g' is acceleration due to gravity and has a value of 9.8 m/s².
Now, weight of the object is given as the product of its mass and acceleration due to gravity. So, replace 'mg' by weight 'w'. So, the equation becomes,
[tex]\Delta U = w(h_f-h_i)[/tex]
Now, rewriting in terms of 'w', we get:
[tex]w=\dfrac{\Delta U}{(h_f-h_i)}[/tex]
Now, plug in all the given values and solve for 'w'. This gives,
[tex]w=\dfrac{-3900\ J}{(0-5.31)\ m}\\\\\\w=\dfrac{3900}{5.31}\ N\\\\\\w=734.46\ N[/tex]
Therefore, weight of the vaulter is 734.46 N.
