At the base of a vertical cliff, a model rocket, starting from rest, is launched upwardsatt= 0 with a time-varying acceleration given byay(t) =A−BtwhereAandBare positive constants. Also att= 0, a small stone is released from restfrom the top of the cliff at a heighthdirectly above the rocket. (This heighthis higherthan the maximum height reached by the rocket.) The stone hits the rocket at theinstant when the rocket reaches its maximum height. The gravitational acceleration ofmagnitudegis downward. You may neglect air resistance. Determine an expressionfor the initial heighthfrom which the stone was dropped in terms of the constantsA, B, andg