3) A motorcyclist is speeding trying to reach the top of a 20-m-high vertical cliff. He/she reaches a platform tilted upward at an angle of 30 degrees from the hori- zontal and he/she leaves the platform at a speed of 44 m/s. The cliff is 70 m away. Will he/she go over the top of the cliff?

Q: The incenter of a triangle is equidistant from its sides. true or false?

A: Ans--- TRUE  The incenter of a triangle is the point on the interior of the triangle that is…

Q: Prove that an object thrown at an acute angle of elevation travels along a parabolic path, if wind…

A: To show that the path is parabolic                 ux=u cos θuy=u sin θax=0ay=±g

Q: 3. A 40-cm long car windshield wiper begins in a horizontal position at the base of the windshield…

A: This is trignometry problem

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A: Keeping the distance relative to the ramp constant, it is observed that the knockback distance of…

Q: A particle of mass M is moving in a straight line under constant force of magnitude F and a kv?,…

A:

Q: A 5500-pound vehicle is driven at a speed of 30 miles per hour on a circular interchange of radius…

A: As , f=mv2rGiven , m=5500 pound ,v=30 miles/hr , r=100 feetv=44 ft/s

Q: Exercise 8. Show that the sum of the angles of a geodesic triangle on a surface of positive…

A: We will use the Gauss–Bonnet theorem to prove the given statement.

Q: The cables of a horizontal suspension bridge are supported from two towers 40ft high and 150ft…

A: Given Bridge are supported by two towers Height of the tower=40 feet Distance between two tower=150…

Q: A gutter having a triangular cross section is to be made by bending in the middle of a strip of…

A: Here is the solution of the given problem.

Q: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

Q: Find the length of the midsegment of this trapezoid (show all work on paper): 14 22 X =

A:

Q: A package that weighs 200 lb is placed on an inclined plane. If a force of 80 lb is just sufficient…

A:

Q: A truck has to pass under an overhead parabolic arch bridge which has a span of 20 meters and is 16…

A: Given,           A truck has to pass under an overhead parabolic arc bridge which has a span of 20…

Q: A bullet is fired from the ground at an angle of 60◦ above the horizontal.What initial speed v0 must…

A: given: A bullet is fired from the ground at an angle of 60◦ above the horizontal. What initial speed…

Q: A truck has to pass under an overhead parabolic arch bridge 20 meters and is 16 meters high. If the…

A:

Q: 3. Two like parallel forces 38 N and 86 N are acting at a distance of 12 cm. What is the position of…

A: Consider the point at which resultant of the forces will act, is 'x' m from the point P. Thus the…

Q: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft…

A:

Q: A railroad rail is I kilometer long and it expands on a hot day 10 centimeters in length.…

A: please see the next step for solution

Q: man at point A on the shore of a circular lake of radius 1 km wants to reach point B on the shore…

A:

Q: A flexible tube of length 4 m is bent into an L-shape. Where shouldthe bend be made to minimize the…

A: A flexible tube of length 4m is bent into an L-shape. Let x,y be the length of sides of L-shape.…

Q: A helicopter is to fly directly from a helipad at the origin in the directionof the point (1, 1, 1)…

A: Given that: A helicopter is to fly directly from a helipad at the origin in the direction of the…

Q: A ball is thrown from a height of 6ft at an angle of 60 degrees with the horizontal. If the ball…

A: Initial Speed in horizontal directionux= v cos 600initial speed in vertical directionuy = v sin…

Q: A fish is reeled in at a rate of 1 foot per second from a bridge 15 ft. above the water. At what…

A:

Q: 2. A 20 ft. ladder is placed against a wall that the foot of the ladder is 4 ft. from the base of…

A: Now, we have a 20 feet ladder.  It is placed against a wall and is 4 feet away from the base of the…

Q: Suppose you apply a force of 80 N to a 0.25-meter-long wrench attached to a bolt in a direction…

A: This question is related to vector,  directions, magnitude and torque calculations. We will solve it…

Q: A plane travels from point A on a bearing 150° to a point B 10 km from A as illustrated above. How…

A: We are given the following information. We need to find AC.

Q: 1)If the 15 kilogram object is resting on a table tilted at 40 °. indicate the decomposition of the…

A: Consider the provided question,

Q: What is the ideal speed to take a 75 m radius curve banked at a 40.0° angle? m/s

A: Given,

Q: A mass of 10 kg is suspended by two pieces of string 30cm and 40 cm long from two points that are 50…

A: We are given with Length of string 1 (AC)= 30cm Length of string 2 (BC) =40cm Distance between two…

Q: On a bicycle you have two pulleys. Even though they have proper names let's call them the pedal gear…

A: A)The circumference of the pedal gear is given by:So for every revolution the gear chain moves 4π…

Q: (16) Say, a guy dumped by his (only) girlfriend. He wants to jump off from a building of 240 ft.…

A: Consider the provided question, (a) Solving for horizontal and vertical velocity components. As the…

Q: A window whose height is 5ft is on a wall such that its bottom edge is 3 ft above your eye level.…

A:

Q: An airplane is traveling at a speed of 130 km/hr with a bearing of 10° at a fixed altitude with…

A:

Q: The lower edge of a mural, 12 feet high, is 6 feet above the observer's eyes. Under the assumption…

A:

Q: The wheels of a bicycle have radius 15 cm and are rotating at 140 rpm. Find the  speed of the bike…

A: We know,

Q: Compute for the tangential velocity of a wheel rotating at a speed of 2000 rpm such that the radius…

A: Formula for tangential velocity Vt is: Vt=2πrt  here r is the radius of the wheel and t is the time…

Q: A drive has a maximum speed of 12,000 revolutions per minute. If a disc has a diameter of 12 cm​,…

A: Given 5000 revolutions per minute

Q: A trough, 10 ft long, has semi-elliptical ends which are 3 feet deep and 4 feet wide. If the trough…

A:

Q: 2. How much work is done when a hoist lifts a 200-kg rock to a height of 3 m?

A:

Q: A truck has to pass under an overhead parabolic arc bridge which has a span of 20 meters and is 16…

A:

Q: A railroad rail is I kilometer long and it expands on a hot day 10 centimeters in length.…

A: To find the height of the centre of the rail rise above the ground.

Q: A box of mass m=3.0kg slides down a smooth incline plane of 5.0m long with angle. Please find the…

A:

Q: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft…

A:

Q: A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is…

A: The lines that trace the center of the spheres will form a square pyramid. See figure below.

Q: Which is the complete formula used to find the radius of curvature?

A:

Q: Suppose you apply a force of 20N to a 0.25​-meter-long wrench attached to a bolt in a direction…

A:

Q: 3. From the main entrance of a park, there are two pathways where visitors can walk along going to…

A: Given that  The pathways are both tangent to the garden whose center is 12 m away from the entrance…

Q: Derive the equation of torsion and discuss its usefullness and limitations in detail ?

A:

Q: 3. A railroad rail is 1 kilometer long and it expands on a hot day 10 centimeters in length.…

A: Consider the following figure For a small angle x in radians tanx≈sinx≃x Use this to create an…

Q: A 10cm diameter disk emits light uniformly from its surface. 20 cm from this disk, along its axis,…

A: Here we will find the diameter of shadow,

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.