Exam 4: Kinematics in Two Dimensions

A rescue plane flying horizontally at spots a survivor in the ocean directly below and releases an emergency kit with a parachute. . Because of the shape of the parachute, it experiences insignificant horizontal air resistance. If the kit descends with a constant vertical acceleration of how far away from the survivor will it hit the waves?

A boy throws a rock with an initial velocity of 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?

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?

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?

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 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] + [3.0 m - (2.00 m/s²)t²] , where all quantities are in SI units. What is the magnitude of the acceleration of the object at time t = 2.00 s?

If an object travels at a constant speed in a circular path, the acceleration of the object is

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 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?

While an object is in projectile motion (with upward being positive) with no air resistance

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

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

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?

Object A has a position as a function of time given by _A(t) = (3.00 m/s)t + (1.00 m/s²)t² . Object B has a position as a function of time given by _B(t) = (4.00 m/s)t + (-1.00 m/s²)t² . All quantities are SI units. What is the distance between object A and object B at time

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?

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

The horizontal coordinates of a in a strong wind are given by 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 accurate to the nearest

An aircraft performs a maneuver called an "aileron roll." During this maneuver, the plane turns like a screw as it maintains a straight flight path, which sets the wings in circular motion. If it takes it 35 s to complete the circle and the wingspan of the plane is 11 m, what is the acceleration of the wing tip?

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?