To determine the value of d, we can analyze the motion of the two balls using the laws of motion and the principles of free fall.
Let's consider the motion of the first ball, which is dropped from a height of 4h. The time it takes for an object to fall freely from a certain height can be calculated using the equation:
t1 = √(2d1/g)
where t1 is the time taken, d1 is the distance fallen (4h in this case), and g is the acceleration due to gravity.
Now, let's consider the motion of the second ball, which is dropped from a height of h. The time it takes for this ball to fall can be calculated using the same equation:
t2 = √(2d2/g)
where t2 is the time taken, and d2 is the distance fallen by the second ball (which we need to determine).
Since we want both balls to hit the ground at the same time, t1 should be equal to t2. Therefore, we can equate the two equations:
√(2d1/g) = √(2d2/g)
Squaring both sides of the equation, we get:
2d1/g = 2d2/g
Canceling out the g terms, we have:
d1 = d2
Substituting the values of d1 and d2, we get:
4h = d
Therefore, to ensure that the balls hit the ground at the same time, the distance fallen by the first ball (d1) should be equal to the distance fallen by the second ball (d2), which means that d should be equal to 4h.