Question 1

Solve the problem.
-What is the minimum force required to prevent a ball weighing 17.2 lb from rolling down a ramp which is inclined 24.8° with the horizontal? Round to the nearest tenth.

Accepted Answer

The minimum force required to prevent the ball from rolling down is the component of the weight parallel to the ramp. This is calculated as 17.2 lb * sin(24.8°), which is approximately 7.2 lb.

Question 2

Solve the problem.
-A force of 659 lb is required to pull a boat up a ramp inclined at 15.0° with the horizontal. How much does the boat weigh? Round to the nearest pound.

Accepted Answer

The force required to pull the boat up the ramp is the component of the boat's weight parallel to the ramp. Using the formula: Force = Weight * sin(incline angle), we have 659 lb = Weight * sin(15°). Solving for Weight gives approximately 2550 lb.

Question 3

Solve the problem.
-Suppose you would like to cross a 207-foot wide river in a boat. Assume that the boat can travel 37 mph relative to the water and that the current is flowing west at the rate of 7 mph. What bearing should be chosen so
That the boat will land at a point exactly across from its starting point? Give your answer to the nearest tenth of
A degree.

Accepted Answer

To counteract the 7 mph westward current, the boat must have an eastward component of velocity equal to 7 mph. Using trigonometry, the angle θ can be found using sin(θ) = 7/37, which gives θ ≈ 10.9°.

Question 4

Find the absolute value of the complex number.
-8 - 7i

Accepted Answer

The answer of Find the absolute value of the complex...

Question 5

Solve the problem.
-Two people are carrying a box. One person exerts a force of 121 pounds at an angle of 43° with the horizontal. The other person exerts a force of 90 pounds at an angle of 51.6°. Find the weight of the box to the nearest
Pound.

Accepted Answer

The answer of Solve the problem.
-Two people are carrying a...

Question 6

Solve the problem.
-A box weighing 65 lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 23 lb. What angle, to the nearest degree, does the first rope make with the vertical?

Accepted Answer

The answer of Solve the problem.
-A box weighing 65 lb...

Question 7

Find the absolute value of the complex number.
-11 + i

Accepted Answer

The answer of Find the absolute value of the complex...

Question 8

Find the absolute value of the complex number.
-9 + 2i

Accepted Answer

The answer of Find the absolute value of the complex...

Question 9

Solve the problem.
-An airplane flies on a compass heading of 90.0° at 480 mph. The wind affecting the plane is blowing from 295° at 23.0 mph. What is the true course and ground speed of the airplane? Round results to an appropriate number
Of significant digits.

Accepted Answer

The answer of Solve the problem.
-An airplane flies on a...

Question 10

Find the absolute value of the complex number.
--5 + 5i

Accepted Answer

The answer of Find the absolute value of the complex...

Question 11

Solve the problem.
-A basketball player shoots the ball with a velocity of 12.8 ft/s at an angle of 40.8° with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Accepted Answer

The horizontal component of the velocity can be found using the formula: horizontal component = velocity * cos(angle). Therefore, 12.8 ft/s * cos(40.8°) ≈ 9.7 ft/s.

Question 12

Graph the complex number.
-

Accepted Answer

The answer of Graph the complex number.
-
...

Question 13

Graph the complex number.
-

Accepted Answer

The answer of Graph the complex number.
-
...

Question 14

Solve the problem.
-A pilot wants to fly on a bearing of 61.1°. By flying due east, he finds that a 50-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane to the nearest mile per hour.

Accepted Answer

To find the airspeed of the plane, we use vector addition. The wind vector is 50 mph north, and the resultant vector is at a 61.1° bearing. The plane's airspeed vector must be such that when added to the wind vector, it results in the desired bearing. Using trigonometry, the eastward component of the plane's airspeed must counteract the northward wind component to achieve the 61.1° bearing. Solving for the airspeed using the cosine of the angle gives approximately 91 mph.

Question 15

Solve the problem.
-Suppose you would like to cross a 210-foot wide river in a boat. Assume that the boat can travel 37 mph relative to the water and that the current is flowing west at the rate of 7 mph. If the bearing is chosen so that the
Boat will land at a point exactly across from its starting point, how long will it take for the boat to make the
Crossing? Give your answer to the nearest second.

Accepted Answer

The answer of Solve the problem.
-Suppose you would like to...

Question 16

Find the absolute value of the complex number.
-4 - i

Accepted Answer

The answer of Find the absolute value of the complex...

Question 17

Graph the complex number.
-

Accepted Answer

The answer of Graph the complex number.
-
...

Question 18

Solve the problem.
-One rope pulls a barge directly east with a force of 77 N, and another rope pulls the barge directly north with a force of 44 N. Find the magnitude of the resultant force acting on the barge. Round to the nearest Newton.

Accepted Answer

The resultant force can be found using the Pythagorean theorem: √(77² + 44²) ≈ 89 N.

Question 19

Graph the complex number.
-

Accepted Answer

The answer of Graph the complex number.
-
...

Question 20

Graph the complex number.
-

Accepted Answer

The answer of Graph the complex number.
-
...

Quiz 7: Applications of Trigonometry

Solve the problem. -What is the minimum force required to prevent a ball weighing 17.2 lb from rolling down a ramp which is inclined 24.8° with the horizontal? Round to the nearest tenth.

Solve the problem. -A force of 659 lb is required to pull a boat up a ramp inclined at 15.0° with the horizontal. How much does the boat weigh? Round to the nearest pound.

Find the absolute value of the complex number. -8 - 7i

Solve the problem. -Two people are carrying a box. One person exerts a force of 121 pounds at an angle of 43° with the horizontal. The other person exerts a force of 90 pounds at an angle of 51.6°. Find the weight of the box to the nearest Pound.

Solve the problem. -A box weighing 65 lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 23 lb. What angle, to the nearest degree, does the first rope make with the vertical?

Find the absolute value of the complex number. -11 + i

Find the absolute value of the complex number. -9 + 2i

Solve the problem. -An airplane flies on a compass heading of 90.0° at 480 mph. The wind affecting the plane is blowing from 295° at 23.0 mph. What is the true course and ground speed of the airplane? Round results to an appropriate number Of significant digits.

Find the absolute value of the complex number. --5 + 5i

Solve the problem. -A basketball player shoots the ball with a velocity of 12.8 ft/s at an angle of 40.8° with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Graph the complex number. -

Graph the complex number. -

Solve the problem. -A pilot wants to fly on a bearing of 61.1°. By flying due east, he finds that a 50-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane to the nearest mile per hour.

Find the absolute value of the complex number. -4 - i

Graph the complex number. -

Solve the problem. -One rope pulls a barge directly east with a force of 77 N, and another rope pulls the barge directly north with a force of 44 N. Find the magnitude of the resultant force acting on the barge. Round to the nearest Newton.

Graph the complex number. -

Graph the complex number. -