Homework Answers
Concept - use energy conservation principle to find the relation between velocities as shown below. The horizontal component of acceleration will always be zero. Because acceleration is only downwards due to acceleration due to gravity.
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9. The figure below shows the trajectory of a ball undergoing projectile motion. The time t-0s...
A ball is thrown from the ground onto a roof of height yroof 16 m from...
A ball is thrown from the ground onto a roof of height yroof 16 m from a distance of x 7 meters away as shown in the diagram to the left. The maximum height of the ball's trajectory is ymax 3.2 meters above the top of the roof. Standard Exercise Roof Toss Standard Exercse Cliff Toss 1) Find the required initial vertical component of the velocity, V vy 0 m/s Submit Help 2) Find the time for the ball to...
Use the figure to answer questions 13-14. The figure represents the parabolic trajectory of a ball...
Use the figure to answer questions 13-14. The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity ofthe ball is v, at an angle θ to the horizon. The vertical dashed lines represent equal time interval, Δ e x(m) 13) The horizontal velocity at point c is A) B) C) 0 Vo cos (0) V. sin (0) D) E) V. depends on what g is along...
Q2. A) Projectile motion (General launch angle): Select any one of the options as answer A...
Q2. A) Projectile motion (General launch angle): Select any one of the options as answer A football kicker is attempting a field goal from 44 m out. The ball is kicked and just clears the lower bar with a time of flight of 2.9 s. If the angle of the kick was 45°, what was the initial speed(Vo) of the ball, assuming no air resistance? a) 21.5 m/s b) 19.7 m/s c) 2.2 m/s d) 39 m/s (Hint: x-Xo =...
Problem 4: A projectile is fired with an initial velocity of 54.1 m/s, at an initial...
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A ball at ground level is thrown straight up with a speed of 12 m/s. How...
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Vector function problem(Calculus 3) 8) A soccer ball is kicked from the point F(0) (0,0,0) with...
Vector function problem(Calculus 3)
8) A soccer ball is kicked from the point F(0) (0,0,0) with an initial velocity of v(0)(0,80,80) ft/s. The spin on the ball produces a constant acceleration of 1.2 ft/s2 in the x-direction. (Hint: The acceleration due to gravity is g 32 ft/s2. It acts in the downward/negative z direction. So the total constant acceleration on the ball is a(t) (1.2,0,-32).) 0 a) Find the velocity and position vectors for t b) Make a sketch of...
2. A baseball thrown from the outfield, a golf ball, or a thrown football, all will follow a trajectory (path) that has horizontal as well as vertical displacement components. If we neglect the a...
2. A baseball thrown from the outfield, a golf ball, or a thrown football, all will follow a trajectory (path) that has horizontal as well as vertical displacement components. If we neglect the air friction on the ball, the path will be a perfect parabolic trajectory. The equations for the displacement of the ball are: Take gravity g as 9.81 meters per second, and the initial velocity, Vo, equal to 35 meters/second. Use Excel to show the ball trajectory for...
Allison throws a tennis ball at time t = 0 from a height h above the...
Allison throws a tennis ball at time t = 0 from a height h above the ground equal to her own height. We assume that the positive horizontal direction is the positive x-direction, and the positive vertical direction is the positive y-direction. The ball has a positive initial horizontal velocity vx, and no initial vertical velocity. At times t1 and t2, the ball bounces on the ground for the first, and second times respectively after being thrown. We assume that...
1. (10 points A Monte Carlo analysis can be used for optimization. For example, the trajectory...
1. (10 points A Monte Carlo analysis can be used for optimization. For example, the trajectory of a ball can be computed with 2vo cos2 Go where y is the achieved height in meters (m), 6% is the initial angle (radians), is the horizontal distance (m), g is the gravitational acceleration (-9.81 m/s2), vo is the initial velocity (m/s), and yo is the initial height. Given yo 1 m, vo 25 m/s, and 500 (or T/180 x 50 rad), determine...
EXAMPLE 7.9 Maximum height of a home-run ball imum height of a projectile launched with ORO...
EXAMPLE 7.9 Maximum height of a home-run ball imum height of a projectile launched with ORO Earlier in ample 3.5) we derived an exression for de m initial speed the initial angle ignoring air resistance Video Tutor Solut 2 Now let's derive this expression using a conservation of energy analysis. Final point Velve- SOLUTION SET UP There are no sonconservative forces the work done by gravity is accounted for in the potential energy terms. As shown in Figure 7.30, we...
A ball is thrown from the ground onto a roof of height yroof 16 m from a distance of x 7 meters away as shown in the diagram to the left. The maximum height of the ball's trajectory is ymax 3.2 meters above the top of the roof. Standard Exercise Roof Toss Standard Exercse Cliff Toss 1) Find the required initial vertical component of the velocity, V vy 0 m/s Submit Help 2) Find the time for the ball to...
Use the figure to answer questions 13-14. The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity ofthe ball is v, at an angle θ to the horizon. The vertical dashed lines represent equal time interval, Δ e x(m) 13) The horizontal velocity at point c is A) B) C) 0 Vo cos (0) V. sin (0) D) E) V. depends on what g is along...
Q2. A) Projectile motion (General launch angle): Select any one of the options as answer A football kicker is attempting a field goal from 44 m out. The ball is kicked and just clears the lower bar with a time of flight of 2.9 s. If the angle of the kick was 45°, what was the initial speed(Vo) of the ball, assuming no air resistance? a) 21.5 m/s b) 19.7 m/s c) 2.2 m/s d) 39 m/s (Hint: x-Xo =...
Problem 4: A projectile is fired with an initial velocity of 54.1 m/s, at an initial inclination of 33.7 degrees with the horizontal r-axis. All initial variables (displacement and time) start at 0. You are asked to consider two cases of motion for the projectile, one without drag, and one with drag, with both the cases including effects of gravity. a) For motion with no drag, acceleration vector is given as а -g, where g 9.8 m/s. b) For motion...
A ball at ground level is thrown straight up with a speed of 12 m/s. How long does it take the ball to reach the maximum height? 0.82 s 1.02 s 0.63s 1.22 s What is the maximum height reached by the ball? 5.10 m 3.26 m 7.34 m 1.96 m The vertical component of the acceleration of a projectile remains constant during the entire trajectory of the projectile. True False For a projectile launched horizontally, the horizontal component of...
Vector function problem(Calculus 3)
8) A soccer ball is kicked from the point F(0) (0,0,0) with an initial velocity of v(0)(0,80,80) ft/s. The spin on the ball produces a constant acceleration of 1.2 ft/s2 in the x-direction. (Hint: The acceleration due to gravity is g 32 ft/s2. It acts in the downward/negative z direction. So the total constant acceleration on the ball is a(t) (1.2,0,-32).) 0 a) Find the velocity and position vectors for t b) Make a sketch of...
2. A baseball thrown from the outfield, a golf ball, or a thrown football, all will follow a trajectory (path) that has horizontal as well as vertical displacement components. If we neglect the air friction on the ball, the path will be a perfect parabolic trajectory. The equations for the displacement of the ball are: Take gravity g as 9.81 meters per second, and the initial velocity, Vo, equal to 35 meters/second. Use Excel to show the ball trajectory for...
1. (10 points A Monte Carlo analysis can be used for optimization. For example, the trajectory of a ball can be computed with 2vo cos2 Go where y is the achieved height in meters (m), 6% is the initial angle (radians), is the horizontal distance (m), g is the gravitational acceleration (-9.81 m/s2), vo is the initial velocity (m/s), and yo is the initial height. Given yo 1 m, vo 25 m/s, and 500 (or T/180 x 50 rad), determine...
EXAMPLE 7.9 Maximum height of a home-run ball imum height of a projectile launched with ORO Earlier in ample 3.5) we derived an exression for de m initial speed the initial angle ignoring air resistance Video Tutor Solut 2 Now let's derive this expression using a conservation of energy analysis. Final point Velve- SOLUTION SET UP There are no sonconservative forces the work done by gravity is accounted for in the potential energy terms. As shown in Figure 7.30, we...
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