Three-dimensional motion Consider the motion of the following objects. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical and opposite g, the ground is horizontal, and only the gravitational force acts on the object unless otherwise stated.a. Find the velocity and position vectors, for t ≥ 0.b. Make a sketch of the trajectory.c. Determine the time of flight and range of the object.d. Determine the maximum height of the object. A golf ball is hit east down a fairway with an initial velocity of⟨50, 0, 30⟩ m/s. A crosswind blowing to the south produces anacceleration of the ball of -0.8 m/s2.

4. Swims across Lake Erie are officially sanctioned by the Lake Erie Open Water Swimming Association. Your friend on the swim team wants to swim across the lake. The plan is that your friend will swim to Presque Isle starting at a location at Long Point, Ontario which is 24 miles due north of Presque Isle. You will be navigating a boat with a GPS. Your friend can maintain a speed of 1.80 mph in still water. All during the swim you observe that objects drifting in the water are moving at 0.70 mph to the east due to the current. a. What bearing should you maintain? That is what direction should you point the boat to reach Presque Isle? Give your answer relative to a compass direction (i.e., 30° north of west). Hint, you want your net velocity vector to be straight south. b. How long did it take your friend to swim across Lake Erie? c. What is the addition amount of time that your friend will need to swim compared to if there was no current (assume your friend swims at a constant rate)?

An airplane takes off and flies upward at an angle of 21° with a constant speed of 262 m/s. While the plane is flying upward, a piece of the engine falls off when the plane reaches a height of 860 m. a) How long does it take the piece of the engine to reach the ground? Give your answer in seconds. b) What is the horizontal distance covered by the piece of the engine before it lands? Give your answer in meters.

An owl is carrying a mouse to the chicks in its nest. The owl is at that time is 4 m west and 12 m above the center of the 35 cm diameter nest, and flying east at 3.6 m/s at an angle 34° below the horizontal when it accidentally drops the mouse. a.)Calculate the horizontal position of the mouse when it has fallen 12 m, assuming the nest is at the origin of a coordinate system with east being positive.   b.) How far from the east edge of the nest did the mouse fall, in centimeters?

A river flows due south with a speed of 2.8 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.9 m/s due east. The river is 600 mm wide. a-What is the magnitude of his velocity relative to the earth? b-What is the direction of his velocity relative to the earth? c-How much time is required to cross the river? d-How far south of his starting point will he reach the opposite bank?

A ball weighing 0.45 kg in a 0-g environment has an initial speed of 30 m/s at an angle 0 = 35°. It hits the ground for a brief second At =0.07s and bounces away with the same speed at the same angle as shown but now it is moving upward. a) Label the initial and final velocity vectors and find their components in the x hat and y hat directions. b) Find the acceleration vector. c) Find the normal force on the ball and draw it in the diagram. Lo ܘܢ

As the launching angle of the projectile increases, a. Horizontal acceleration increases. b. Vertical acceleration increases. c. The vertical distance the projectile travels per second is constant. d. Vertical acceleration stays the same.

1. Draw a vector to represent each of the following physical quantities. Choose an appropriate coordinate system. a. A displacement of 40 km in the negative y-direction. b. A velocity of 30 m/s at 5° below the negative x-axis. C. An acceleration of 5 m/s² due east. d. A force of 30 N at 15° south of west.

4. A ball is projected with an initial upward velocity component of 80 ft/sec and a horizontal velocity component of 100 ft/sec. a) Find the position and velocity of the ball after 2sec, 3 sec and 6 sec. b) How long a time is required to reach the highest point of trajectory? c) How high is this point? d) How long a time is required for the ball to return to its original level? e) How far has it traveled horizontally during this tme. Show your results in a neat sketch to show all features cearly.

a.) Find the x-component of the velocity, where the x-direction is east. b.) Find the y-component of the plane's velocity, where the y-direction is north.