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Question

The height h cm, reached by a ball thrown vertically upwards is proportional to the square of the of the speed., V metres per second, with which it is thrown. When V= 4 and h =80.

1. Explain why the formula connecting h and V is h = 5V2

ii Find the height reached by a ball thrown upwards at 6 meters per second.

iii the speed with which a ball is thrown if it reaches a height of 20 meters.

Answer 1

velocity = 4 when h= 80

h=kv^2

80 = k(4)^2 = 16k

k= 80/16 = 5

h(v) = 5v^2

height when v=6 is h(6) = 5(6)^2 = 5(36)= 180 meters

20(v) = 5v^2

v^2 = 20/5 = 4

v = sqr4 = 2 m/sec = velocity when height = 20 meters