A ball, dropped vertically, falls d metres in t seconds. D is directly proportional to the square of t. The ball drops 80 metres in the first 4 seconds. How far does the ball drop in the next 8 seconds?

640 m.

Step-by-step explanation:

D = kt^2 where d is the constant of proportionality.

D = 80 m when t = 4 seconds so:

80 = k*4^2

k = 80 / 16 = 5.

So the equation of motion is D = 5t^2.

When t = 8+4 = 12 seconds D = 5*12^2 = 5*144

= 720 m

So the distance the ball drops in the next 8 seconds = 720 - 80

= 640 m.