Concept explainers
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi= 18.0 m/s. The cliff is h = 50.0 m above a body of water as shown in Figure P3.19. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity of the stone? (c) What is the appropriate analysis model for the vertical motion of the stone? (d) What is the appropriate analysis model for the horizontal motion of the stone? (e) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. (f) Write symbolic equations for the position of the stone as a function of time. (g) How long after being released does the stone strike the water below the cliff? (h) With what speed and angle of impact does the stone land?
(a)
The coordinates of the initial position of the stone .
Answer to Problem 19P
The coordinates of the initial position of the stone are
Explanation of Solution
Write the expression for the initial position of the stone.
Here,
Conclusion:
Substitute
Therefore, the coordinates of the initial position of the stone are
(b)
The components of the initial velocity of the stone .
Answer to Problem 19P
The components of the initial velocity of the stone are
Explanation of Solution
Write the expression for the initial velocity of the stone,
Here,
Conclusion:
Substitute
Therefore, the components of the initial velocity of the stone are
(c)
The vertical motion of the stone .
Answer to Problem 19P
The vertical motion of the stone is
Explanation of Solution
In this case, the vertical motion of the stone is equal to the free fall motion.
It is with a constant downward acceleration.
Here,
Conclusion:
Substitute
Therefore, the vertical motion of the stone is
(d)
The horizontal motion of the stone .
Answer to Problem 19P
The horizontal motion of the stone is
Explanation of Solution
In this case, the constant velocity motion in the horizontal direction.
Conclusion:
Thus, there is no horizontal acceleration from gravity.
Therefore, the horizontal motion of the stone is
(e)
The symbolic equations for the
Answer to Problem 19P
The symbolic equations for the
Explanation of Solution
Write the expression for the horizontal final velocity of the stone.
Here,
Write the expression for the vertical final velocity of the stone.
Here,
Conclusion:
Substitute
Substitute
Therefore, the symbolic equations for the
(f)
The symbolic equations for the position of the stone as a function of time .
Answer to Problem 19P
The symbolic equations for the position of the stone as a function of time are
Explanation of Solution
Write the expression for the horizontal final position of the stone.
Here,
Write the expression for the vertical final position of the stone.
Here,
Conclusion:
Substitute
Substitute
Therefore, the symbolic equations for the
(g)
The time of impact of the stone .
Answer to Problem 19P
The time of impact of the stone is
Explanation of Solution
Write the expression for the vertical final position of the stone.
Here,
Rewrite the above equation,
Conclusion:
Substitute
Therefore, the time of impact of the stone is
(h)
The speed and angle of impact of the stone land .
Answer to Problem 19P
The speed and angle of impact of the stone land are
Explanation of Solution
In this case, at the time of impact
The vertical component velocity of the stone,
Substitute
Write the expression for the final velocity of the stone.
Here,
Write the expression for the angle of impact of the stone.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the speed and angle of impact of the stone land are
Want to see more full solutions like this?
Chapter 3 Solutions
Principles of Physics
- A basketball player is standing on the floor 10.0 m from the basket as in Figure P3.47. The height of the basket is 3.05 m, and he shoots the ball at a 40.0 angle with the horizontal from a height of 2.00 m. (a) What is the acceleration of the basketball at the highest point in its trajectory? (b) At what speed must the player throw the basketball so that the ball goes through the hoop without striking the backboard?arrow_forwardA fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of i = 30.0 above the horizontal as shown in Figure P3.18. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building? Figure P3.18arrow_forwardOlympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .arrow_forward
- *Draw a simple diagram representation for the solution.In a game war, one team sets base on a cliff 15m high and 60m away from the opponent’s base. At what velocity must the attack be launched so that the lower base will be hit? The initial launch is at 20 degrees below the horizontal?arrow_forwardA cannon launches a cannonball from level ground with an initial speed of 80 m/s at an angle of 280 above the horizontal. What horizontal distance does the cannonball travel when the cannonball returns to the ground? Given the same initial velocity of launch, at what other angle above the ground can the cannonball be fired and achieve the same horizontal range as before? (Assume that g = 9.81 m/s2.) a. Range = 540 m, and angle = 420 above the horizontal b. Range = 600 m, and angle = 620 above the horizontal c. Range = 270 m, and angle = 620 above the horizontal d. Range = 540 m, and angle = 620 above the horizontal e. Range = 270 m, angle = 420 above the horizontalarrow_forwardA marble is launched from the edge of a table at a angle of 45 ° up from horizontal and goes through the air until it hits the floor. True or False? For such a marble, |vx| (the magnitude of the x-component of the velocity) is decreasing the entire time the marble is airborne.arrow_forward
- A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity relative to himself. If has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?arrow_forwardIn an article on the use of the sling as a weapon, the author states that a skilled slinger can sling a rock a distance of about 384 m. What is the minimum speed the rock must have when it leaves the sling to travel exactly 384 m? To solve this problem it will be necessary to first determine the required launch angle of the projectile. What launch angle must the projectile have in order to find the minimum speed required to achieve a given horizontal distance?arrow_forwardA projectile is launched with a launch angle of 30° with respect to the horizontal direction and with an initial speed of 26 m/s. How do the vertical and horizontal components of the projectile's velocity vary with time?The initial velocity in the x-direction vx0 is related to the initial speed by vx0 = v0 cos 30°. The constant velocity in the x-direction means that the equation describing the time dependence of x for the particle, with x0 taken as 0, is x = x0 + vx0t = 0 + m/s t. The equation for the vertical coordinate, which is constantly accelerating downward at g = 9.8 m/s2, is y = y0 + vy0t − 1 2 gt2 = m/s t + m/s2 t2.arrow_forward
- A projectile is fired at 75 degrees above the horizontal line with an initial velocity v0. At which of the following angles the projectile will land at the same distance as it is landed when fired at 75 degrees? A. 15 degrees B. 25 degrees C. 35 degrees D. 45 degreesarrow_forwardStanding at the edge of a 70 meter high cliff, Failee throws a rock with a horizontal velocity of 21 m/s. How long is the rock in the air, and how far does it travel horizontally before striking the water ?arrow_forwardAn inflatable life raft is released from an airplane at 300 m altitude, in level flight, with an air speed of 100 m/s in the horizontal direction. At what horizontal distance from the release point does the raft strike the water?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning