Exam 3: Motion in Two or Three Dimensions

A long-distance swimmer is able to swim through still water at 4.0 km/h. She wishes to try to swim from Port Angeles, Washington, directly north to Victoria, British Columbia, a distance of 50 km. An ocean current flows through the Strait of Juan de Fuca from west to east at 3.0 km/h. In what direction (relative to north) should she swim to make the crossing along a straight line between the two cities?

A plane flying at 70.0 m/s suddenly stalls. If the acceleration during the stall is 9.8 m/s² directly downward, the stall lasts 5.0 s, and the plane was originally climbing at 25° to the horizontal, what is the velocity after the stall?

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Compare the time it takes each of them to reach the lake below.

A plane has an eastward heading at a speed of 156 m/s (relative to the air). A 20.0 m/s wind is blowing southward while the plane is flying. The velocity of the plane relative to the ground is

A boy throws a rock with an initial velocity of 2.15 m/s at 30.0° above the horizontal. If air resistance is negligible, how long does it take for the rock to reach the maximum height of its trajectory?

A satellite orbits the earth a distance of 1.50 × 10⁷ m above the planet's surface and takes 8.65 hours for each revolution about the earth. The earth's radius is 6.38 × 10⁶ m. The acceleration of this satellite is closest to

A wind farm generator uses a two-bladed propeller (see figure) mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A small piece from the tip of the propeller breaks off when the propeller is vertical. At that instant, the period of the motion of the propeller is 1.2 s. The fragment flies off horizontally, falls with negligible air resistance, and strikes the ground at P. (a) How far is point P from the base of the pylon? (b) At what angle with respect to the vertical is the fragment moving just as it strikes the ground at P?

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

A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of v0_x = 60.0 m/s and v0_y = 175 m/s, as shown in the figure. The projectile rises and then falls into the sea at point P. The time of flight of the projectile is 40.0 s, and it experiences no appreciable air resistance in flight. What is the height of the cliff?

An airplane is flying at a speed of 2.00 10² m/s in level flight at an altitude of 8.00 10² m. 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?

A child throws a ball with an initial speed of 8.00 m/s 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?

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 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?

Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 7.00 revolutions every 10.0 seconds. What is the magnitude of the acceleration of the ball?

An object has a position given by = [2.0 m + (3.00 m/s)t]î + [3.0 m - (2.00 m/s²)t²]ĵ, where all quantities are in SI units. What is the magnitude of the acceleration of the object at time T = 2.00 s?

The horizontal coordinates of a Frisbee™ in a strong wind are given by x = -12t + 4t² and y = 10t - 3t², where x and y are in meters, and t is in seconds. (a) What is the acceleration of the Frisbee? Give a magnitude and a direction, measuring angles from the positive x direction. (b) What is the magnitude of the velocity at t = 2.0 s, accurate to the nearest m/s?

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 swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s, during which time she is swept downstream 480 m. (a) How fast can she swim in still water? (b) What is the speed of the current?