Q...A man in a balloon rising vertically with an acceleration of 4.9 m/s2 releases a ball 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the ball is:

a. 14.7 m b. 19.6 m c. 9.8 m d. 24.5 m

Let Ub and Vb be the velocities at t=0 and t=2 for the balloon

And accelaration of balloon(Ab)=4.9=g/2 m/s2

Vb=Ub+(Ab)t       (Ub=0)

from this we get, Vb=g m/s   (Upwards)

and from ,s=(Ub)t+(1/2)(Ab)t^2          (where s is the hieght at which the ball is dropped)

we get s=g meters

when the ball is dropped its initial velocity is gm/s upwards(due to balloon)

hence velocity of ball at ground(using third eq of motion):

V^2=g^2 + 2(g)(g)        (since,,initial vel of ball=g m/s,,,acc due to gravity=g m/s2,,,displacement=g meters)

v^2=3g^2------------------------------------1

If we want to find the greatest hieght(to which it rises)then it should rebound back with same velocity(elastic collision)

therfore ,

v^2=u^2-2(g)(H)---------------------------2   (Where H is the max hieght it reaches)

in this case v=0 since at the greatest hieght the vel of ball is zero

and u^2=3g^2  (from eq--1)

therefore

eq 2 becomes:

3g^2=2gs

ie,s=3/2(g)=14.7m

Approved

b is the answer. is am i right

while releasing the ball the balloon was at a height of 9.8m from the ground and was rising up at 9.8m/s.

so the maximum height raised by the ball is 9.8 + (9.8)²/2*9.8 = 14.7m

the answer is a. 14.7m