In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is h . The mug slides off the counter and strikes the floor at distance d from the base of the counter.
(a) With what velocity did the mug leave the counter?
(b) What was the direction of the mug's velocity just before it hit the floor?
The height of the counter is h and the mug slides off the counter and strikes the floor at distance d from the base of the counter.
The rate of change of an object's location with regard to a frame of reference is its velocity, which is a function of time. A statement of an object's speed and direction of motion is referred to as velocity.
The initial angle is and the initial height is .
The component of motion is constant in horizontal projectile motion, but the component rises in magnitude:
The mug's velocity components at the instant of collision with the ground are:
The velocity angle at the instant of contact may be computed as follows:
An outfielder throws a baseball to his catcher in an attempt to throw out a runner at home plate. The ball bounces once before reaching the catcher. Assume the angle at which the bounced ball leaves the ground is the same as the angle at which the outfielder threw it as shown in Figure P4.74, but that the ball's speed after the bounce is one-half of what it was before the bounce.
(a) Assume the ball is always thrown with the same initial speed and ignore air resistance. At what angle should the fielder throw the ball to make it go the same distance with one bounce (blue path) as a ball thrown upward at with no bounce (green path)? (b) Determine the ratio of the time interval for the one-bounce throw to the flight time for the no-bounce throw.
A pendulum with a cord of length swings in a vertical plane (Fig. P4.70).When the pendulum is in the two horizontal positions and localid="1663633590926" , its speed is . Find the magnitude of (a) the radial acceleration and (b) the tangential acceleration for these positions. (c) Draw vector diagrams to determine the direction of the total acceleration for these two positions. (d) Calculate the magnitude and direction of the total acceleration at these two positions.
A moving beltway at an airport has a speed and a length L . A woman stands on the beltway as it moves from one end to the other, while a man in a hurry to reach his flight walks on the beltway with a speed of relative to the moving beltway.
(a) What time interval is required for the woman to travel the distance L ?
(b) What time interval is required for the man to travel this distance?
(c) A second beltway is located next to the first one. It is identical to the first one but moves in the opposite direction at speed . Just as the man steps onto the beginning of the beltway and begins to walk at speed relative to his beltway, a child steps on the other end of the adjacent beltway. The child stands at rest relative to this second beltway. How long after stepping on the beltway does the man pass the child?
A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of at an angle of below the horizontal. It strikes the ground later.
(a) How far horizontally from the base of the building does the ball strike the ground?
(b) Find the height from which the ball was thrown.
(c) How long does it take the ball to reach a point below the level of launching?
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