Question 571501
Physics textbooks show that the trajectory of a ball that rolls of a table is a parabola with drop proportional to the square of the horizontal distance.
Let x be the horizontal distance covered as the ball is dropping (in m).
Let y be the drop distance (in m).
{{{y=kx^2}}}
Substituting y=0.3 and x=3
{{{0.3=k*3^2}}} --> {{{0.3=9k}}} --> {{{k=0.3/9}}} --> {{{k=1/30}}}
(a) for x=6, {{{y=(1/30)6^2}}} --> {{{y=36/30}}} --> {{{y=1.2}}}
The ball drops 1.2 m as it moves 6 m horizontally.
(b) for y=2.5 {{{2.5=(1/30)x^2}}} --> {{{x^2=30*2.5}}} --> {{{x^2=75}}} --> {{{x=5sqrt(3)}}} = approximately 8.7
The ball has moved 8.7 m horizontally as it dropped 2.5 m.