15.0 m
Explanation:
We can solve the problem by using the law of conservation of energy.
At the beginning, all the energy of the system is stored in the elastic potential energy of the compressed spring, which is given by
[tex]E=\frac{1}{2}kx^2=\frac{1}{2}(4500 N/m)(0.60 m)^2=810 J[/tex]
When the spring is released, the pumpkin of mass m=5.5 kg is pushed upwards. All the energy is then converted into gravitational potential energy of the pumpkin when it reaches its maximum height h:
[tex]E=mgh[/tex]
Re-arranging the equation, we can find h:
[tex]h=\frac{E}{mg}=\frac{810 J}{(5.5 kg)(9.8 m/s^2)}=15.0 m[/tex]
