Question

a remote control airplane flew along at a velocity of 48 ft/s at an angle of 32° above the horizontal. find the magnitudes of the horizontal and vertical components of the velocity. (round your answers to the nearest tenths)
magnitude of the horizontal component of the velocity = choose...
magnitude of the vertical component of the velocity = choose...
90.6 ft/s
40.7 ft/s
25.4 ft/s
56.6 ft/s
given the arithmetic sequence:
244, 187, 130, ...
find the 16th term.
select one:
a. -668
b. 1156
c. -611
d. 1099

Explanation:

Part 1: Velocity Components

Step1: Recall velocity component formulas

For a velocity $v$ at an angle $\theta$ above horizontal, horizontal component $v_x = v\cos\theta$, vertical component $v_y = v\sin\theta$. Here, $v = 48$ ft/s, $\theta = 32^\circ$.

Step2: Calculate horizontal component

$v_x = 48\cos(32^\circ)$. $\cos(32^\circ) \approx 0.8480$, so $v_x \approx 48 \times 0.8480 \approx 40.7$ ft/s.

Step3: Calculate vertical component

$v_y = 48\sin(32^\circ)$. $\sin(32^\circ) \approx 0.5299$, so $v_y \approx 48 \times 0.5299 \approx 25.4$ ft/s.

Part 2: Arithmetic Sequence 16th Term

Step1: Find common difference $d$

In arithmetic sequence $244, 187, 130, \dots$, $d = 187 - 244 = -57$ (or $130 - 187 = -57$).

Step2: Use arithmetic sequence formula

The $n$th term formula is $a_n = a_1 + (n - 1)d$. Here, $a_1 = 244$, $d = -57$, $n = 16$.

Step3: Calculate 16th term

$a_{16} = 244 + (16 - 1)(-57) = 244 + 15 \times (-57) = 244 - 855 = -611$.

Answer:

Horizontal component: $40.7$ ft/s, Vertical component: $25.4$ ft/s