You are on a train that is traveling at 3.0 m/s along a level straight track. Very near and parallel to the track is a wall that slopes upward at a 12° angle with the horizontal. As you face the window (0.777 m high, 2.26 m wide) in your compartment, the train is moving to the left, as the drawing indicates. The top edge of the wall first appears at window corner A and eventually disappears at window corner B. How much time, in seconds, passes between appearance and disappearance of the upper edge of the wall? B 3.0 m/s 12⁰

A pilot heads his jet due east. The jet has a speed of 450 mi/h relative to the air. The wind is blowing due north with a speed of 40 mi/h. Assume that the i vector points east, and the j vector points north. Find the true velocity of the jet as a vector.

One of the tasks of the Mighty Hercules was to protect the town of Nemea from a lion.  One day Hercules sees the lion 320 feet away.  He strings his bow and lets an arrow fly.  The arrow leaves his bow travelling at 210 feet per second from a height of 6 feet.  He wants to hit the lion in the neck above the shoulders which is 4 feet off of the ground.   determine the launch angle that will hit the Lion. Find the right angle.

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of  v0 = 17.0 m/s.  The cliff is h = 47.0 m above a flat, horizontal beach as shown in the figure. A student stands on the edge of a cliff with his hand a height h above a flat stretch of ground below the clifftop. The +x-axis extends to the right along the ground and the +y-axis extends up from the ground to the top of the cliff. The origin O of the coordinate plane is directly below the student's hand where the base of the cliff meets the flat ground. The student throws a stone horizontally rightward with initial velocity vector v0. The stone falls with a parabolic trajectory, hitting the ground with a velocity vector v that points down and right. Vector g points straight down. (a) What are the coordinates of the initial position of the stone? x0 =   m y0 =   m (b) What are the components of the initial velocity? v0x =   m/s v0y =   m/s (c) Write the equations for the x-…

I start walking. The 1st leg of my trip I walk dA =95m at θA=21° south of east. The 2nd leg of my trip I walk. dB=95m at θB =27° north of east. On my final leg I walk dC =85m at θC=58° north of west. Choose the coordinate system so that x is directed towards the east, and y is directed towards the north. What is magnitude of my displacement vector (in meters) as measured from the origin, and what is the angle of my displacement vector as measured counter clockwise from the x-axis.

A wall clock has a minute hand with a length of 0.46 m and an hour hand with a length of 0.26 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x axis pointing to 3 o'clock and the positive y axis pointing to 12 o'clock. Write the vector that describes the displacement of a fly if it quickly goes from the tip of the minute hand to the tip of the hour hand at 3:00 P.M. (Let D represents the displacement of the fly.) D = 0.46 |× mî+ -0.26 Let the +y direction be straight up and the +x direction be to the right. Recall the definition of displacement, and remember that positions are vector quantities.

First, a woman walks 25 m in a direction 49° north of east. Then she walks 23 m heading 15° north of east. Finally, she turns and walks 32 m in a direction 68° south of east. What is the total distance she covers? What is her total displacement?

Problem 3-44a: Three vectors A, B, and C have X components of -7.0, -3.0, 0.0, respectively, and y components of -3.0, 5.0, 8.0, respectively. Find the magnitude of A + B + C. Problem 3-44b: Find the direction of A + B + C in degrees. (NOTE: angles are entered as values between 0° and 180°.)

At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 8.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 55.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?  yards (b) What if? The receiver that catches the football travels 64.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?

A car comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side the car is on is 20.3 mm above the river, whereas the opposite side is a mere 1.6 mm above the river. The river itself is a raging torrent 57.0 mm wide. For help with math skills, you may want to review: Vector Magnitudes For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Different initial and final heights. a.  How fast should the car be traveling just as it leaves the cliff in order to just clear the river and land safely on the opposite side? Express your answer in meters per second. b.  What is the speed of the car just before it lands safely on the other side? Express your answer in meters per second.