In 2.10 h, a balloon drifts 16.9 km north, 5.16 km east, and 3.23 km upward from its release point on the ground. Find (a) the magnitude of its average velocity and (b) the angle its average velocity makes with the horizontal. (a) Number 8.55 (b) Number 79.63 Units Units km/h *(degrees)
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- A ferryboat is traveling in a direction 22.0° north of east with a speed of 3.16 m/s relative to the water. A passenger is walking with a velocity of 2.53 m/s due east relative to the boat. What is (a) the magnitude and (b) the direction of the velocity of the passenger with respect to the water? Give the directional angle relative to due east. (a) Number i IN (b) Number MI Units UnitsYou drive 5.50 km in a straight line in a direction 25° East of North. (a) Find the distances you would have to drive straight East and then straight North to arrive at the same point. (This is equivalent to finding the components of the displacement along the East and North directions.) km East km North(b) Show that you still arrive at the same point if the East and North legs are reversed in order.A whale swims due east for a distance of 6.95 km, turns around and goes due west for 1.87 km, and finally turns around again and heads 6.37 km due east. (a) What is the total distance traveled by the whale? (b) What is the magnitude of the displacement of the whale? (a) Number Units (b) Number Units
- A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 17.0t and y = 4.20t − 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time = m/s(c) obtain the expression for the acceleration vector as a function of time = m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.24 s. = m = m/s = m/s2At 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 plane flies 488 km east from city A to city B in 41.0 min and then 883 km south from city B to city C in 1.20 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east).
- For this problem, you can think of the jet stream as a river of air. Across the United States, the jet stream usually moves from west to east. We will assume that the jet stream is moving in its usual direction at 9.00 x 101 km/hr. On a particular day, you need to pilot a plane from one city to another that is 4.50 x 102 km directly to the south. The top speed of the aircraft in still air is 285 km/hr. (a) Make a sketch to represent what is happening in this problem. Label all quantities that you know. (b) Using cardinal directions (north, east, south, west) to give a heading, which direction should you aim the plane to reach the city directly to the south at top speed? (c) How fast (in km/hr) would you be moving relative to the ground? (c) How much time (in hr) will it take you to reach your destination?A hiker walks 3.05 km south and then 2.00 km east, all in 4.00 hours. HINT (a) Calculate the magnitude (in km) and direction (in degrees south of east) of the hiker's displacement during the given time. magnitude direction X km X ° south of east (b) Calculate the magnitude (in km/h) and direction (in degrees south of east) of the hiker's average velocity during the given time. km/h magnitude direction o south of east (c) What was her average speed (in km/h) during the same time interval? km/hThe pilot of an aircraft flies due north relative to the ground in a wind blowing 80 km/h toward the east. If his speed relative to the air is 410 km/h, what is the magnitude of the velocity of his airplane relative to the ground? State the answer to the nearest tenth of the km/h.