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- A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the base is moving away at the rate of 36 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? y 13-ft ladder y(t) x(t) XA 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving away at the rate of 48 fusec a. What is the rate of change of the height of the top of the ladder? Sec b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? 07/ 07/ CELLES y(t) 0 25-ft ladder 0 xit)An inclined plane has angle theta with respect to the vertical. A. Find an expression for the components in the direction of the plane. B. Find an expression for the component of gravity in the direction perpendicular to the plane. C. Sketch figures which illustrate parts a and b above; highlight and label the results.
- The barge of starch passes a light house. From the top of the light house 60 m high from sea level, the angle of depression (AOD) of the barge is 15 degree. A. Find the distance of the barge from the foot of the light house if the AOD is 15 deg. B. If the barge moves 120 m away from the lighthouse, what will be the resulting AOD from the top of the light house? C. If the barge moves 100 m closer to the lighthouse as it approaches to the original position, what is the resulting AOD?a.) Find the angle of the sum of the three vectors shown in the figure, measured counterclockwise from the positive x-axis.A vector is 23.4 m long and makes an angle of 60.0° counterclockwise from the y-axis (on the side of the –x-axis). a.)What is the x-component of this vector? b.)What is the y-component of this vector?
- A vector A = 1ax+1ay, the origin of this vector is the point M (1, 0.5, 1) in Cartesian coordinate system. a. Determine the component of the vector A in the direction of the vector ax b. Determine the dot product A.ay c. Determine cross product A.az d. Determine the angle formed by the vector A and the vector ay. e. Determine the componen ts of this vector in cylindrical coordinate system f. Determine the components of this vector in spherical coordinate systemThe grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled A⃗ A→ through D⃗ D→. This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. A. What is the xcomponent of A→? B.What is the y component of A⃗ ? C.What is the y component of B⃗ ? D.What is the x component of C⃗ ? E. In ordered pair notation, write down the components of vector B⃗ F. In ordered pair notation, write down the components of vector D G.What is true about B⃗ and D⃗ ? They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors.You are given a vector A = 190i and an unknown vector B that is perpendicular to A. The cross-product of these two vectors is A × B = 81k. a. What is the x-component of the vector B? b. What is the y-component of the vector B? c. What can you say about the z-component of vector B?
- 1. The towers of a 60 meter parabolic suspension bridge are 12m high and the lowest point of the cable is 3m above the roadway. Find the vertical distance from the roadway. Find the vertical distance from the roadways to the cable at 15m from the center. a. 4 m b. 5 m c. 6 m d. 7 m 2. If a boy with a single shot, shot a bird flying horizontally at a distance in from the ground with the speed of 12 meters per minute. The boy missed the bird and the bullet of the sling went up to the maximum height h from the level of the bird. When the bullet descended to the range of the projectile, it hit the bird. Find the horizontal component speed of the bullet. a. 15.28 m/min b. 14.484 m/min c. 12.468 m/min d. 16.524 m/min 3. A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 30 ft. If the distance across the top of the mirror is 64 in., how deep is the mirror at the center? a. 32/45 in b. 30/43 in c. 32/47 in d. 35/46 inIf the magnitude of the vector product of two vectors a and b are are equal to 0, then what do we know about a and b? a. they are perpendicular Ob. they are in different directions с. they are in different planes O d. They are parallelProblem: Vector F1 = 625 N makes an angle of 270° when rotated counterclockwise from the +x axis. Vector F2 = 875 N makes a 120° angle from Vector F1 when rotated counterclockwise. Find the following: 1. What is the value for Rx? A. 700 N B. 757.8 N C. 900 N 2. What is the value for Ry? A. -187.5 N B. 200 N C. +187.5 N 3. What is the direction of the vector needed to balance the two forces? A. 0° B. 186° C. -32° D. 166° E. 270° F. -31° G. -180° Answer all the questions please I'll give rate.