Exam 4: Newtons Laws of Motion

Projectiles: 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?

Projectiles: A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of v_0x = 60.0 m/s and v_0y = 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?

Relative velocity: 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?

Two-dimensional motion: 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?

Projectiles: 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?

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

Two-dimensional motion: An electron moves with a constant horizontal velocity of and no initial vertical velocity as it enters a deflector inside a TV tube. The electron strikes the screen after traveling horizontally and vertically upward with no horizontal acceleration. What is the constant vertical acceleration provided by the deflector? (The effects of gravity can be ignored.)

Two-dimensional motion: 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?

Uniform circular motion: 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?

Uniform circular motion: 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

Uniform circular motion: 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

Two-dimensional motion: 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

Projectiles: Jan and Len throw identical rocks off a tall building at the same time. The ground near the building is flat. Jan throws her rock straight downward. Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30°. Len throws the rock with a speed twice that of Jan's rock. If air resistance is negligible, which rock hits the ground first?

Relative velocity: 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?

Relative velocity: 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

Two-dimensional motion: An object has a position given by = [2.0 m + ( 5.00 m/s)t] + [3.0 m - ( 2.00 m/s²)t²] , where quantities are in SI units. What is the speed of the object at time

Projectiles: 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. Just as they reach the lake below

Projectiles: 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?

Projectiles: 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?

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