Catapulting a rock

Question

A rock catapulting through the air is known to have a near perfect parabolic path. The rock lands at a horizontal distance of 170m from its starting point (which is at ground level), just skimming over a 36m high tree situated 25m from the rocks starting position. 

 

Determine by how much the rock will clear if a 50m high tower is located 45m from the landing point. 

Answer 1

A parabola is  nothing but a quadratic equation in cartesian coordinate system..

 

So the equation of the catapulted rock be y=ax^2+bx+c.We have three points given in the problem (0,0 ),(25,36) and (170,0). we know that c=0 because the starting and end points are on the same ground level..The remaining coeficients a and b also can be found by substitution .

1296a+ 36b=25
28900a+ 170bb=0

The values are calculated as a=-0.0051824 and b=0.8810116

Now to check he rock will clear if a 50m high tower is located 45m substitute y=45 we get a quadratic equation.

-0.0051824 *x^2+0.8810116x-45=0. Now determine the value of x.I the value of x is real then the rock will clear.You try by yourself.Another way is maximize y=ax^2+bx+c. to see ymax is >=45 .All the best.