Your car tire is rotating at 4.0 rev/s when suddenly you press down hard on the accelerator. After traveling 300 m, the tire’s rotation has increased to 6.5 rev/s . The radius of the tire is 32 cm.
A) What was the tire’s angular acceleration? Give your answer in rad/s²?
The figure shows the angular-velocity-versus-time graph for a particle moving in a circle.
How many revolutions does the object make during the first 4.0 s?
The total number of radians made by the object is the area under the graph. Based on the given graph, the total number of radians is
Convert this to revolutions, knowing that 2π radians is equal to 1 revolution.
A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 200 m above the glacier at a speed of 190 m/s.
A) How far short of the target should it drop the package?
Alex, a mountaineer, must make it across a wide crevasse. Alex runs horizontally off the edge and successfully makes it to the other side of the crevasse, which is below the point from which he takes off, as shown in the figure.
A) Determine the algebraic sign of Alex’s x velocity and y velocity at the instant he leaves the ground at the edge of the crevasse.
B) Determine the algebraic signs of Alex’s x velocity and y velocity the instant before he safely lands on the other side of the crevasse.
At the buzzer, a basketball player shoots a desperation shot. The ball goes in!
C) Determine the algebraic signs of the ball’s x velocity and y velocity the instant after it leaves the player’s hands.
D) Determine the algebraic signs of the ball’s x velocity and y velocity at the ball’s maximum height.
A rock is thrown with a speed of 12.0 m/s and a launch angle of 30.0° (above the horizontal) travels a horizontal distance of before hitting the ground. Use the value for the free-fall acceleration.
A) Which diagram represents an accurate sketch of the rock’s trajectory?
B) Find the height from which the rock was launched.
C) A second rock is thrown straight upward with a speed of 6.000 m/s. If this rock takes 1.636 s to fall to the ground, from what height H was it released?
The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time corresponds to the moment just after the ball is launched from position and . Its launch velocity, also called the initial velocity, is .
Two other points along the trajectory are indicated in the figure.
One is the moment the ball reaches the peak of its trajectory, at time with velocity . Its position at this moment is denoted by or since it is at its maximum height.
The other point, at time with velocity , corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is , also known as since it is at its maximum horizontal range.
Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which it was launched, as is the case here. Hence .
How do the speeds compare?
You are attempting to row across a stream in your rowboat. Your paddling speed relative to still water is 3.0 m/s (i.e., if you were to paddle in water without a current, you would move with a speed of 3.0 m/s ). You head off by rowing directly north, across the stream. Assume that the stream flows east at 4.0 m/s, determine how far downstream of your starting point you will finally reach the opposite shore if the stream is 6.0 meters wide.