Question

description show all you work, including units, on separate paper. follow the \problem solving method\. this final exam is cumulative and covers material from the entire course. instructions from the list of choices, select the one best answer. multiple attempts not allowed. this test can only be taken once. force completion this test can be saved and resumed later. your answers are saved automatically. * question completion status: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 moving to another question will save this response. question 17 of 62 1.6 points save answer a boy throws a rock with an initial velocity of 2.15 m/s at 30.0° above the horizontal. what is the horizontal component of the inital speed of the rock? 0.925 m/s 2.04 m/s 1.12 m/s 1.86 m/s

Explanation:

Step1: Recall horizontal velocity formula

The horizontal component of velocity \( v_x \) for a projectile motion is given by \( v_x = v_0 \cos\theta \), where \( v_0 \) is the initial velocity and \( \theta \) is the angle with the horizontal.

Step2: Substitute values

Given \( v_0 = 2.15 \, \text{m/s} \) and \( \theta = 30.0^\circ \). So, \( v_x = 2.15 \times \cos(30.0^\circ) \).
We know that \( \cos(30.0^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660 \).
Then \( v_x = 2.15 \times 0.8660 \approx 1.86 \, \text{m/s} \)? Wait, no, wait: Wait, 2.15 cos(30°): 2.15 0.8660254 ≈ 2.15 0.866 ≈ let's calculate 2 0.866 = 1.732, 0.150.866=0.1299, total ≈ 1.732 + 0.1299 = 1.8619? Wait, but wait, the options: 1.86 is an option. Wait, but wait, maybe I miscalculated. Wait, no, wait the angle is 30 degrees, cos(30) is √3/2 ≈ 0.866. So 2.15 0.866 ≈ 1.86. Wait, but let's check again. Wait, 2.15 * cos(30°):

2.15 0.8660254 = 2.15 0.8660254. Let's compute 2 0.8660254 = 1.7320508, 0.15 0.8660254 = 0.12990381, sum is 1.7320508 + 0.12990381 = 1.8619546 m/s, which is approximately 1.86 m/s. Wait, but the options include 1.86 m/s. Wait, but let me check the options again. The options are 0.925, 2.04, 1.12, 1.86. So 1.86 is the answer? Wait, but wait, maybe I made a mistake. Wait, no, horizontal component is v0 cos(theta). So yes, 2.15 * cos(30°) ≈ 1.86 m/s. So the correct answer is 1.86 m/s, which is option D (if options are labeled, but here the last option is 1.86 m/s.

Wait, but wait, let's recalculate: 2.15 * cos(30°):

cos(30°) = √3/2 ≈ 0.8660254038

2.15 0.8660254038 = 2.15 0.8660254038

Calculate 2 * 0.8660254038 = 1.7320508076

0.15 * 0.8660254038 = 0.12990381057

Sum: 1.7320508076 + 0.12990381057 = 1.8619546182 m/s, which is approximately 1.86 m/s. So the answer is 1.86 m/s, which is the last option.

Answer:

1.86 m/s (the option with 1.86 m/s)