Concept explainers
(a)
Find the horizontal displacement of the dart as a function of initial speed.
(a)
Answer to Problem 78PQ
The horizontal displacement of the dart as a function of initial speed is
Explanation of Solution
Write the
Here,
Here,
Conclusion:
Substitute
The above equation is a quadratic and the solution for time will be,
Since time should be position take the positive root then the value of time is,
Substitute
Therefore, the horizontal displacement of the dart as a function of initial speed is
(b)
Find the horizontal displacement with initial velocity of
(b)
Answer to Problem 78PQ
The horizontal displacement with initial velocity of
Explanation of Solution
Use the horizontal displacement equation derived in previous part.
Conclusion:
Substitute
Therefore, the horizontal displacement with initial velocity of
(c)
Find the horizontal displacement with initial velocity of
(c)
Answer to Problem 78PQ
The horizontal displacement with initial velocity of
Explanation of Solution
Use the horizontal displacement equation derived in previous part.
Conclusion:
Substitute
Therefore, the horizontal displacement with initial velocity of
(d)
Drive the simplified expression for horizontal displacement for small initial velocity.
(d)
Answer to Problem 78PQ
The simplified expression for horizontal displacement for small initial velocity is
Explanation of Solution
When the initial velocity is small then the square of the initial velocity is negligible then equation III becomes.
Therefore, the simplified expression for horizontal displacement for small initial velocity is
(e)
Drive the expression for horizontal displacement for high initial velocity.
(e)
Answer to Problem 78PQ
The expression for horizontal displacement for high initial velocity is
Explanation of Solution
When the initial velocity is high then the
Therefore, the expression for horizontal displacement for high initial velocity is
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Chapter 4 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A World War II bomber flies horizontally over level terrain with a speed of 275 m/s relative to the ground and at an altitude of 3.00 km. The bombardier releases one bomb. (a) How far does the bomb travel horizontally between its release and its impact on the ground? Ignore the effects of air resistance. (b) The pilot maintains the planes original course, altitude, and speed through a storm of flak. Where is the plane when the bomb hits the ground? (c) The bomb hits the target seen in the telescopic bombsight at the moment of the bombs release. At what angle from the vertical was the bombsight set?arrow_forwardAt t=0, a projectile is launched from ground level with an initial speed of vi. at t=1.5s, it is displaced d=33 m horizontally from the launch point and h=25m above the launch point. let +x be to the right and +y upward. Ignore air resistance. a) what is the x component of v0x of the projectiles velocity immediately after it is launched? b) what is the y component voy of the projectile's velocity after it is launched? c) what is the maximum height reached above the ground?arrow_forwardA person stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 15.0 m/s. The stone leaves his hand at a height of h = 52.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the stone leaves the hand. (a) What are the coordinates of the initial position of the stone? (Enter your answers in m.) (b) What are the components of the initial velocity? (Enter your answers in m/s.) (c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Assume that vx and vy are in m/s and t is in seconds. Do not include units in your answers.) (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Assume that x and y are in meters and t is in seconds. Do not include units in…arrow_forward
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- ANSWER THE LETTER D, E, AND F ONLY From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 6.50 m/s and angle of 25.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. (c) Find the equations for the x- and y-components of the position as functions of time. (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown. (f) How long does it take the ball to reach a point 12.0 m below the level of launching?arrow_forwardA fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 2.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (25.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = ay = (b) What is the direction of its acceleration with respect to unit vector î? Draw coordinate axes on a separate piece of paper, and then add the acceleration vector with its tail at the origin. Write the numerical values for the x and y components and then use this drawing to determine the angle.° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 28.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axisarrow_forwardA supply plane flies horizontally with a speed of 100 m/s and an altitude of 350 m. Use g = -10 m/s/s. A) What are the initial velocity components of an object that is dropped from the plane at the instant it is dropped? B) How fast is an object that is dropped from the plane traveling 7.5 seconds later? C) What angle, below the horizontal, does the velocity vector of an object that is dropped from the plane make 7.5 seconds later? D) How long does it take for an object that is dropped from the plane to hit the ground when air resistance is neglected? E) How far does an object that is dropped from the plane travel in the horizontal direction?arrow_forward
- A person stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of v0 = 17.5 m/s. The rock leaves his hand at a height of h = 45.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the rock leaves the hand. (a) What are the coordinates of the initial position of the rock? (Enter your answers in m.) x0= m y0= m (b) What are the components of the initial velocity? (Enter your answers in m/s.) v0x= m/s v0y= m/s (c) Write the equations for the x- and y-components of the velocity of the rock with time. (Use the following as necessary: t. Assume that vx and vy are in m/s and t is in seconds. Do not include units in your answers.) vx=17.5m/s vy=−9.8t m/s (d) Write the equations for the position of the rock with time, using the coordinates in the figure. (Use the following as necessary: t. Assume that x and y are…arrow_forwardAn object rolls off a tabletop with a horizontal velocity v0x = 2.1 m/s. The table is at a height y0 = 0.75 m, above the floor. Use a coordinate system with its origin on the floor directly beneath the point where the object rolls off the table, its horizontal x-axis lying directly beneath the object’s trajectory, and its vertical y-axis pointing up. A. How long, in seconds, is the object falling before it hits the floor? B.How far, in meters, does the object land from the edge of the tabletop? C. What is the vertical component of velocity, in meters per second, when the object hits the ground? Recall that the positive y-direction is upwards. D. What is the magnitude of the velocity (it's speed) when it hits the floor?arrow_forwarda ball is launched with a velocity of magnitude 10.0 m/s, at an angle of 50.0° to the horizontal.The launch point is at the base of a ramp of horizontal length d1 6.00 m and height d2 = 3.60 m. A plateau is located at the top of the ramp. (a) Does the ball land on the ramp or the plateau? When it lands, what are the (b) magnitude and (c) angle of its displacement from the launch point?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning