Exam 3: Motion in Two or Three Dimensions

A hiker throws a stone from the upper edge of a vertical cliff.The stone's initial velocity is 25.0 m/s directed at 40.0° with the face of the cliff,as shown in the figure.The stone hits the ground 3.75 s after being thrown and feels no appreciable air resistance as it falls. (a)What is the height of the cliff? (b)How far from the foot of the cliff does the stone land? (c)How fast is the stone moving just before it hits the ground?

A plane flies directly between two cities,A and B,which are separated by .From A to B,the plane flies into a headwind.On the return trip from B to A,the wind velocity is unchanged.The trip from B to A takes less than the trip from A to B.What is the airspeed of the plane,assuming it is the same in both directions?

A child throws a ball with an initial speed of at an angle of 40.0° above the horizontal.The ball leaves her hand 1.00 m above the ground and experience negligible air resistance. (a)What is the magnitude of the ball's velocity just before it hits the ground? (b)At what angle below the horizontal does the ball approach the ground?

An airplane is flying at a speed of in level flight at an altitude of .A package is to be dropped from the airplane to land on a target on the ground.Ignore air resistance. (a)At what horizontal distance away from the target should the package be released so that it lands on the target? (b)In what direction relative to the horizontal will the package be traveling when it hits the ground?

An object has a position given by = [2.0 m + (3.00 m/s)t] + ,where all quantities are in SI units.What is the magnitude of the acceleration of the object at time ?

An object moves in a circle of radius R at constant speed with a period T.If you want to change only the period in order to cut the object's acceleration in half,the new period should be

For general projectile motion,when the projectile is at the highest point of its trajectory,

Shown below are the velocity and acceleration vectors for a person in several different types of motion.In which case is the person slowing down and turning to his right?

What is the maximum distance we can shoot a dart,from ground level,provided our toy dart gun gives a maximum initial velocity of and air resistance is negligible?

For an object in uniform circular motion,its velocity and acceleration vectors are always perpendicular to each other at every point in the path.

You want to swim straight across a river that is wide.You find that you can do this if you swim at an angle of θ = 28° from the upstream direction at a constant rate of relative to the water.At what rate does the river flow? The angle θ is measured from the river bank (directly upstream is while directly across the river is

A ball is tied to the end of a cable of negligible mass.The ball is spun in a circle with a radius making 7.00 revolutions every .What is the magnitude of the acceleration of the ball?

An airplane flies between two points on the ground that are 500 km apart.The destination is directly north of the origination of the flight.The plane flies with an air speed of .If a constant wind blows at 10.0 m/s due west during the flight,what direction must the plane fly relative to north to arrive at the destination?

If you set the cruise control of your car to a certain speed and take a turn,the speed of the car will remain the same.Is the car accelerating?

A cart is moving with a constant horizontal velocity of 5.00 m/s.A small pebble is launched from the front of the cart with a velocity of 8.00 m/s at 60.0° above the horizontal as measured relative to the cart (see figure)and experiences no significant air resistance.Just as the pebble returns to the level from which it was launched,its distance from the front of the cart is closest to

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle.Which arrow best represents the direction of the acceleration of the object at point P?

A disk-shaped space station 175 m in diameter spins uniformly about an axis perpendicular to the plane of the disk through its center.How many rpm (rev/min)must this disk make so that the acceleration of all points on its rim is g/2?

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s.and experiences no air resistance.The height of the tabletop above the ground is 2.00 m.What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

A ball is thrown at a 60.0° angle above the horizontal across level ground.It is thrown from a height of 2.00 m above the ground with a speed of 20.0 m/s and experiences no appreciable air resistance.The time the ball remains in the air before striking the ground is closest to

A rock is thrown at a window that is located 18.0 m above the ground.The rock is thrown at an angle of 40.0° above horizontal.The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance.If the rock strikes the window on its upward trajectory,from what horizontal distance from the window was it released?