In Fig. 4-55, a ball is shot directly upward from the ground with an initial speed of . Simultaneously, a construction elevatorcab begins to move upward from the ground with a constant speed of . What maximum height does the ball reach relative to (a) the ground and (b) the cab floor? At what rate does the speed of the ball change relative to (c) the ground and (d) the cab floor?
A) Maximum height of the ball relative to the ground is .
B) Maximum height of the ball relative to the cab floor .
C) Rate of speed change of ball relative to ground .
D) Rate of speed change of ball relative to cab floor.
1) Initial velocity of the ball is .
2) Speed of construction elevator is .
The cab floor and the ball both are under the influence of gravitational force. So, we can use the equations of constant acceleration for their motion. Using the kinematic equations in terms of initial, final velocity, acceleration, and displacement, we can find the height the ball can reach.
When ball reach to the maximum height (h), its final velocity (v) will be zero. The acceleration on the ball is the gravitational acceleration (g) and it is acting in a downward direction. If we assume the upward direction as positive, the gravitational acceleration is considered negative. Therefore, the equation (i) becomes,
Rearranging this for height h we get,
Therefore, the maximum height of the ball relative to the ground is
The cab floor is moving upward with a velocity
So, the relative velocity of a ball is,
Following the similar procedure as part a), we can find the maximum height as
The maximum height the ball reaches relative to the cab floor is
Ball has only gravitational force acting on it, so the acceleration of a ball or its rate of speed change is equal to the acceleration due to gravity that is .
The cab floor is moving with constant velocity, so it will also have similar acceleration as that of ball that is .
In Fig. 4-48a, a sled moves in the negative X direction at constant speed while a ball of ice is shot from the sled with a velocity relative to the sled. When the ball lands its horizontal displacement relative to the ground (from its launch position to its landing position) is measured. Figure 4-48b givesas a function of . Assume the ball lands at approximately its launch height. What are the values of (a)and (b)? The ball’s displacement relative to the sled can also be measured. Assume that the sled’s velocity is not changed when the ball is shot. What is whenis (c) and (d) 15.0 m/s?
Long flights at mid-latitudes in the Northern Hemisphere encounter the jet stream, an eastward airflow that can affect a plane’s speed relative to Earth’s surface. If a pilot maintains a certain speed relative to the air (the plane’s airspeed), the speed relative to the surface (the plane’s ground speed) is more when the flight is in the direction of the jet stream and less when the flight is opposite the jet stream. Suppose a round-trip flight is scheduled between two cities separated by 4000 km, with the outgoing flight in the direction of the jet stream and the return flight opposite it.The airline computer advises an airspeed of 1000 km/hr, for which the difference in flight times for the outgoing and return flights is 70.0 min.What jet-stream speed is the computer using?
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