A train travels 3.5 kilometers on a straight track with a grade of 1.2°, What is the vertical rise of the train in that distance?

Q: A projectile is fired with muzzle speed 150 m/s and angle of elevation 45ofrom a position 10 m above…

A:

Q: A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the…

A: Given: The angle of elevation of the balloon is 65°, and the rate of pulling of rope is 5 ft /s.…

Q: The angular velocity of a wheel is 10 revolutions per second. What is the linear velocity in cm per…

A: Given: Angular velocity=10 revolutions per second……1Diameter =60 cm……2

Q: A gun with muzzle velocity of 1200 ft >/sec is fired at an angle of 8° above the horizontal. Find…

A: It is given that the gun has the velocity 1200 ft/ sec which is fired at angle 8 degree.Compute the…

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second,…

A: Given: A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per…

Q: An airplane took off from an airport and traveled at a constant rate and angle of elevation. When…

A:

Q: Athena kicks a football from the ground with a resultant velocity of 25 m/s at an angle of 47° above…

A:

Q: The radius of the wheel on a bike is 18 inches. If the wheel is revolving at 118 revolutions per…

A: Given radius of wheel on bike=18 inches.Also wheel is revolving at 118 revolutions per minute.To…

Q: Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of…

A: Given, The height of plateau = 50 m The angle of elevation = 20o

Q: A motorboat traveling across a wide river is headed 50 degrees north of west at a rate of constant…

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Q: A projectile is fired with an initial speedof 500 m / sec at an angle of elevation of 45. How high…

A: For projectile motion, the parametric equation for the distance travelled is given by…

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 4 feet per second,…

A: Solution..

Q: A cannon is fired at an angle of 34° with the horizontal. If the cannonball has an initial velocity…

A: From the given information, The angle of projectile from the launch is given as 34°. The initial…

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second,…

A: We have to find the distance between man and his friend.

Q: What two angles of elevation will enable a projectile to reach a target 16 km downrange on the same…

A:

Q: A rock is thrown downward from the top of a building, 168 ft high, at an angle of 60 ◦ with the…

A: Use the displacement formula, x=v0(cos θ)t and substitute v0 with 80 and θ with 60° to get x=40t.…

Q: A loading ramp is 21 meters long with a height of 6 meters. What is the angle of incline that the…

A: Explanation of the answer is as follows

Q: An airplane took off from an airport and traveled at a constant rate and angle of elevation. When…

A: What was the angle when the airplane rose from the ground?

Q: A railway train is travelling on a curve of 1500 mt radius at the rate of 66 kph. Through what angle…

A:

Q: A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15 degree…

A:

Q: Mayon Volcano has a base circumference of 130 km and a height of 2462 meters. Determine its average…

A:

Q: A gun is fired with angle of elevation 30o. What is the muzzle speed if the maximum height of the…

A:

Q: A shell, fired from ground level at an elevation angle of 45 ◦ , hits the ground 24,500 m away.…

A: Given: The shell was fired from the ground at an elevation of θ=45°. Horizontal distance from the…

Q: At what rate is the angle between a clock's minute and hour hands changing at 7 o'clock in the…

A:

Q: What is the wave speed of a wave that has a frequency of 50 Hz and a wavelength of 2.0 m?

A:

Q: What is the length of the trail (

A:

Q: How much work is done by gravity in causing a 45-kg rock to tumble 54 m down a slope at an angle of…

A:

Q: A projectile is fired with an initial speedof 500 m / sec at an angle of elevation of 45. When and…

A:

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second,…

A:

Q: A street slopes downward at an angle of 15° with the horizontal.  A ball is rolling on the street.…

A: Given : A street slopes downward at an angle of 15° with the horizontal. it has covered a horizontal…

Q: The base of an isosceles triangle is 8 feet long. If the altitude is 6 ft long and is increasing 3…

A: Let ABC be an isosceles triangle where x = Base angle, y = Altitude. Given: BC = 8 ft , y=6 and dydt…

Q: The radius of the wheel on a truck is 18 inches. If the wheel is revolving at 274 revolutions per…

A: The radius is 18 inches. The circumference of the wheel is the distance covered in one revolution, 1…

Q: A cannon is fired at an angle of 39° with the horizontal. If the cannonball has an initial velocity…

A: The angle of projectile from the launch is given as 39° The initial velocity is given as 605 ft/s…

Q: You stand 15 feet from the base of a water tower and look un at an angle of 78° at the top of the…

A: Draw the whole situation and mention the angle, hight given than use tangent ratio in the right…

Q: A 12 – meter fire truck ladder leaning on the vertical fence also leans on the vertical wall of a…

A: Given figure is: We have to find BC. From the above figure we have, AC=12 m, AE=4 m, DE=3 m, DE⊥AB…

Q: If you know the cotangent value for a given angle, how can you find the tangent value for that same…

A: The solution is :

Q: A car travels at 70mph and has 28 inch in diameter tires. What is the angular speed of a point on…

A:

Q: The radius of the wheel on a bike is 27 inches. If the wheel is revolving at 144 revolutions per…

A: Given that the radius of wheel is 27 inches.

Q: A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude…

A: Given that a plane flying with a constant speed of 19 km/min passes over a ground radar station at…

Q: A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is its angle of inclination to the nearest…

A: Given, The length of a wheelchair ramp = 4.2m  It rises 0.7 m  We have to find its angle of…

Q: A river has a constant current of 3 kilometers per hour. At what angle to a poat dock should a…

A:

Q: A woman is standing 15 meters away from a 20-meter tall building. At what angle is she looking to…

A: Given that height of building=20 meter a woman standing 15 meters away  find the angle she is…

Q: A wind tower at the top of a hill casts a shadow 30 m long along the side - the hill. An observer at…

A:

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second,…

A:

Q: The radius of the wheel on a truck is 18 inches. If the wheel is revolving at 274 revolutions per…

A: Given: The radius of the wheel on a truck is 18 inches. If the wheel is revolving at 274 revolutions…

Q: A ball is thrown with an initial velocity of 70 km per second, at an angle of 35° with the…

A:

Q: A rocket is shot into the air at an angle of 60°. If it is traveling at 200 ft per second, how high…

A: Speed of rocket=200ft/sec Angle at which rocket is shot=60o To find the height of rocket from ground…

Q: A gun with a muzzle velocity of 1040 ft/ sec is fired at an angle of 16° above the horizontal. Find…

A: Given that muzzle velocity = 1040 ft/secangle θ=16° above the horizontal To find : the horizontal…

Q: A kite is flying at a height of 65 m attached to a string. If the inclination of the string with the…

A:

Q: A person is sitting watching TV. What is the height of the entire screen (in grey shadow)?

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.