SAT Math Multiple Choice Question 935: Answer and Explanation
3. A cannonball is shot out of a cannon at a 45° angle with an approximate speed of 283m/s. The cannon from which the ball was fired sits on the edge of a cliff, and itsheight above the ground is 20 meters. The equations given above represent the cannonball'sheight above the ground (y) and its horizontal distance (x) from the face of the cliff, t seconds after it was fired, where t ≥ 0. How many seconds after the ball was fired does its vertical height above theground equal its horizontal distance from the cliff?
- A. 1
- B. 2
- C. 3
- D. 4
Correct Answer: B
Category: Passport to Advanced Math / Quadratics
Strategic Advice: In real-world scenarios, a good bit of the text is probably just providing the context of the question. Be sure to focus on what the question is asking (here, find t when x and y are equal).
Getting to the Answer: Because both equations are given in terms of t, set the two equations equal to each other and simplify:
The resulting equation is quadratic, so you can either factor and solve, or use square rooting:
Time can't be negative, so t must equal 2. This matches (B).