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for velocity after grabbing the box,

the collision is not explicitly stated to be elastic or inelastic, so we can only be sure that momentum is conserved. (no net external force of the system as the system is girl + box)

therefore

p= m*v

use momentum before grabbing the box to solve for velocity after grabbing the box, given that the mass changed.

The second part of your answer is wrong.

You can not use conservation of energies but instead must use momentum to get an accurate answer.

m(initial) * v(initial)= m(final) * v(final)

:. 60*4.98 = 75 * v(final)

:. v after grabbing the box = 3.98m/s

The third part of your answer is also wrong....

You cannot use the previous value found for the Kinetic energy!

you must find Ke max at the point of grabbing the box which is equal to

:. 0.5(60 +15) * 3.98^2 = 594.015

This value becomes Potential max so

:. 594.015 = m*g*h(max)

:. 594.015/(75*9.8) = 0.808184

To get final height fro top of trampoline add the height at which the box was grabbed (2.0m)

:. 2.0 + 0.808184 = 2.81m

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