Bill and Ben are on a bridge, timing how long it takes stones they have dropped to hit the water below.  A quadratic relation can be used to determine the distance, D, in metres, that ta stone will fall in the time, t, in seconds after it is realeased.  In this relation, a = -0.5g, where g is acceleration due to gravity, which is approximately 9.8 m/s² on Earth.  Ben starts a timer when Bill releases a stone, and he stops the timer when the stone hits the water below.  The mean time of serveral trials is 3 s.

a) Determine a quadratic function that models the falling stones.

b) How high above the water are Bill and Ben? Explain your answer.

c) On Saturn's moon, Titan, the value of g is 1.35 m/s^2.  Suppose that Bill and Ben are astronauts and they are standing at the top of a cliff on Titan.  If they record the time for a stone to fall from their hands to the bottom of the cliff as 3 s, how high is the cliff, to the nearest hundreth of a metre?

A jet skier leaves a dock at 8 a.m. and travels due west at 36 km/h. A second jet skier leaves the same dock 10 min later and travels due south at 44 km/h. At what time of day, to the nearest minute, will the two jet skis be 20 km apart? 

Determine the measrue of angle x in the diagram. Be sure to explain your reasoning.

 $94.7°$9‍4.7° is the angle at the top

 In Alberta, ramps that are designed for people using mobility devices must meet certain safety requirments. One such requirment is that the angle between the ramp and the horizontal must be less than 4.8°. Explain whether or not the ramp below is acceptable. 

Explain why knowing a combination of four pairs of equal sides or equal angles guarantees one of the congruence relationships.

Troy has written a proof showing that the diagonals of a parallelogram are equal in length. The diagonals of a parallelogram are not necessarily equal so Troy must have made an error. Identify and explain his error.

Statement   |  Justification

AB = ED       |     Opposite sides of parallelogram

BAE = AED   |      Alternate interior angles

ABD = BDE   |     Alternate interoir angles

ABC = EDC   |   ASA

BC = EC      |   Corresponding sides of congruent angles

AC = DC      |   Corresponding sides of congruent angles

AE = BD      |   AC + CE = DC + CB

Larry likes skeet shooting, where a clay disc is shot into the air and the participant tries to shoot it as it flies through the air. The discs are released from a firing mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120m on a parabolic path. The average maximum height a disc reaches is 40m.

sketch a diagram that represents it with a equation that represents the flight of the clay disc. 

Determine the domain and range of the quadratic equation.