If an object is accelerating, can the net force acting on it be zero?

No, the net force cannot be zero.

Explanation:

From newton's second law,

ΣFnet = ma

Since a is accelerating I.e it is change velocity with respect to time taken, since acceleration can only occur when the force acting on the body is not balanced.

Then Fnet cannot be zero.

Now, if Fnet is zero

Fnet = ma=0

It shows that, the acceleration is zero. So since the body is accelerating, then the net force can not be zero

the maxium height is 34m/s