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Question 1 of 15

1. Which of the following variables are known?

Question 1 of 15

Question 2 of 15

2. In part (a) which speed is asked?

Question 2 of 15

Question 3 of 15

3. Let's consider a general case where the angle \(\theta\geq 0\) and the following coordinate system.

*inserte acá el coordinate system*

 

Which of the following equations describes the motion in the X direction?

Question 3 of 15

Question 4 of 15

4. Now, which of the following equations best describes the motion in the y-direction?

Question 4 of 15

Question 5 of 15

5. Now, we have two equations, one in the vertical direction and one horizontal. Both of them have the time; should we use time as an implicit or an explicit variable?

Question 5 of 15

Question 6 of 15

6. Use the vertical and horizontal motion equations to find just one time-independent equation. Which of the following equations is equivalent to yours? (Hint: solve the horizontal motion equation for t, and replace this equation in the vertical motion equation. Remember to use the trigonometric identities and to consider the coordinate system.)

Question 6 of 15

Question 7 of 15

7. We have all the numerical values of the equation to find the initial speed.

Question 7 of 15

Question 8 of 15

8. Replace in the last equation found the angle of the first case and the initial positions; then, solve for the initial speed. Which of the following equations is equivalent to yours?

Question 8 of 15

Question 9 of 15

9. Which of the following statements are true?

Question 9 of 15

Question 10 of 15

10. Replace the numerical values in the initial speed equation. The initial speed of the dart is   \(\text{m/s}\).

Question 10 of 15

Question 11 of 15

11. To find the second trial angle, let's come back to the time-independent equation we found before. Use the trigonometric identities to have an equation that only depends on the \(\tan\theta\). Find an equation of the form \(a(\tan\theta)^2+b(\tan\theta)+c=0\). Which of the following equations is equivalent to yours?

Question 11 of 15

Question 12 of 15

12. Search for the solutions of the quadratic equation, using the general solution formula for a quadratic equation. Which of the following equations is equivalent to yours?

Question 12 of 15

Question 13 of 15

13. Which of the following statements are true?

Question 13 of 15

Question 14 of 15

14. When you solve this kind of equation, quadratic formula, you have to possible solutions. Are both solutions physically possible?

Question 14 of 15

Question 15 of 15

15. Replace the numerical values in the equation and solve for \(\theta\). The two possible angles are (the smallest)  \(^o\) and (the biggest)\(^o\).

Question 15 of 15