Exam 3: Motion in Two or Three Dimensions

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

An electrical motor spins at a constant 2857.0 rev/min. If the armature radius is 2.685 cm, what is the acceleration of the outer edge of the armature?

A plane flies directly between two cities, A and B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes 65 min less than the trip from A to B. What is the airspeed of the plane, assuming it is the same in both directions?

You want to swim straight across a river that is 76 m 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 1.5 m/s relative to the water. At what rate does the river flow? The angle θ is measured from the river bank (directly upstream is θ = 0° while directly across the river is θ = 90°).

Object A has a position as a function of time given by _A(t) = (3.00 m/s)tî + (1.00 m/s2)t2ĵ. Object B has a position as a function of time given by _B(t) = (4.00 m/s)tî + (-1.00 m/s²)t²ĵ. All quantities are SI units. What is the distance between object A and object B at time t = 3.00 s?

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 catapult is tested by Roman legionnaires. They tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units): Range = 0.20 km; angle of launch = π/4; landing height = launch height. What is the initial velocity of launch of the boulders if air resistance is negligible?

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point with no air resistance. What was the angle of launch?

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?

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) How far from where the child is standing does the ball hit the ground? (b) How long is the ball in flight before it hits the ground?

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

A hockey puck slides off the edge of a table at point A with an initial velocity of 20.0 m/s and experiences no air resistance. The height of the tabletop above the ground is 2.00 m. (a) What is the speed (not the velocity) of the puck just before it touches the ground? (b) What is the distance between point A and the point where the puck hits the ground?

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 120 m/s. 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?

A small boat is moving at a velocity of 3.35 m/s when it is accelerated by a river current perpendicular to the initial direction of motion. If the acceleration of the current is 0.750 m/s², what will be the new velocity of the boat after 33.5 s?

What is the maximum distance we can shoot a dart, from ground level, provided our toy dart gun gives a maximum initial velocity of 2.78 m/s 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.

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

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food? Air resistance is small enough to be ignored.

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

An electron moves with a constant horizontal velocity of 3.0 × 10⁶ m/s and no initial vertical velocity as it enters a deflector inside a TV tube. The electron strikes the screen after traveling 17.0 cm horizontally and 40.0 cm vertically upward with no horizontal acceleration. What is the constant vertical acceleration provided by the deflector? (The effects of gravity can be ignored.)