F4 phy question

For the 1st ball, we have, using the equation: v = u + at
v1 = gt where v1 is its speed aftertime of t seconds, g is the acceleration due to gravity
and, using equation: s = ut + (1/2)at^2
s1 = (g/2)t^2

Similarly for the 2nd ball,
v2 = g(t-1) as the time of travel for the second ball is 1 s less than the first
and s2 = (g/2)(t-1)^2

Hence, v1 - v2 = gt - g(t-1) = g
Because g is a constant, the difference in speed thus remains unchanged.

s1 - s2 = (g/2).[t^2 - (t-1)^2] = (g/2).[t^2 - t^2 + 2t - 1] = (g/2).( 2t-1)
Thus the difference in the balls' separation increases with time of travel t.

The answer is clearly option C.

The answer is C
Let me show you the explaination by calculation
When t=1
The speed of ball A =u+at=0+(10)(1)==10ms^-1
The distance ball A travelled=ut+1/2at^2 =0+(5)(1)^2=5m
The speed of ball B = 0 ms^-1
The distance ball B travelled=0m
The difference between their speeds=10-0=10
The separation between the balls=5
When t=2
The speed of ball A =u+at=0+(10)(2)==20ms^-1
The distance ball A travelled=ut+1/2at^2 =0+(5)(2)^2=20m
The speed of ball B =u+a(t-1)=0+(10)(1)==10ms^-1
The distance ball B travelled=ut+1/2a(t-1)^2 =0+(5)(1)^2=5m
The difference between their speeds=20-10=10
The separation between the balls=20-5=15
When t=3
The speed of ball A =u+at=0+(10)(3)==30ms^-1
The distance ball A travelled=ut+1/2at^2 =0+(5)(3)^2=45m
The speed of ball B =u+a(t-1)=0+(10)(2)==20ms^-1
The distance ball B travelled=ut+1/2a(t-1)^2 =0+(5)(2)^2=20m
The difference between their speeds=30-20=10
The separation between the balls=45-20=25
Conclusion:The separation between the balls increases and the difference between their speeds remains constant.

The answer is A.
Because it said that the two balls are of the same mass and same size and air resistance is negligible.
That means the force that are acting on the balls is the acceleration due to gravity only.

as the mass of the two balls are the same, they have the same acceleration.

As the acceleration is constant,the difference between their speed and the separation between the balls is constant too.

Hope that helps you.