A rocket is launched at an angle of 59.0° above the horizontal with an initial speed of 96 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 28.0 m/s. At this tim its engines fail and the rocket proceeds to move as a projectile. (a) Find the maximum altitude reached by the rocket. (b) Find its total time of flight. (c) Find its horizontal range.
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- A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. ( m/s) + ( m/s) At the maximum height, the speed of the cannon ball is v = m/s and the magnitude of its acceleration is a = m/s2. The time needed to reach maximum height is t = s. The maximum height reached by the cannon ball is H = m.A football is placed at rest on the field with initial coordinates x0 = 0 and y0 = 0. The ball is then kicked and thereby given an initial velocity of magnitude v0 = 23.6 m/s and direction θ0 = 36.3o above the horizontal. Ignore the effects of air resistance. Initial horizontal component of the velocity v0x = Initial vertical component of the velocity v0y = Horizontal component of the acceleration ax = Vertical component of the acceleration ay = Enter the equation for the horizontal position versus time, x(t) = Enter the equation for the vertical position versus time, y(t) = Enter the equation for the horizontal velocity versus time, vx(t) = Enter the equation for the vertical velocity versus time, vy(t) = Enter the equation for the total velocity versus time, v(t) = Enter the equation for the angle of the velocity vector versus time, θ(t)= Enter the maximum height of the football Enter the range of the football Enter the time it takes for the football to reach its maximum…A stone is catapulted at time t 0, with an initial velocity of magnitude 20.0 m/s and at an angle of 40.0° above the horizontal. What are the magnitudes of the (a) horizontal and (b) vertical components of its displacement from the catapult site at t =1.10 s? Repeat for the (c) horizontal and (d) vertical components at t =1.80 s, and for the (e) horizontal and (f) vertical components at t = 5.00 s.
- A particle initially located at the origin has an acceleration of = 1.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). (b) Find the velocity of the particle at any time t. (c) Find the coordinates of the particle at t = 3.00 s. (d) Find the speed of the particle at t = 3.00 s.At one instant a bicyclist is 40.0 m due east of a park’s flagpole, going due south with a speed of 10.0 m/s.Then 30.0 s later, the cyclist is 40.0 m due north of the flagpole, going due east with a speed of 10.0 m/s. For the cyclist in this 30.0 s interval, what are the (a) magnitude and (b) direction of the displacement, the (c) magnitude and (d) direction of the average velocity, and the (e) magnitude and (f) direction of the average acceleration?A stone is catapulted at time t = 0, with an initial velocity of magnitude 20.5 m/s and at an angle of 40.2° above the horizontal. What are the magnitudes of the (a) horizontal and (b) vertical components of its displacement from the catapult site at t = 1.13 s? Repeat for the (c) horizontal and (d) vertical components at t = 1.77 s, and for the (e) horizontal and (f) vertical components at t = 5.47 s. Assume that the catapult is positioned on a plain horizontal ground.
- A particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 5.00 s.x = my = m(d) Find the speed of the particle at t = 5.00 s. m/sA projectile is projected from the origin with a velocity of 25.0 m/s at an angle of 50.0 degrees above the horizontal. What is the time of maximum height of the projectile? Multiple Choice 3.45 s 2.03 s 3.01 s 1.95 s 2.67 sDominador, who is standing on the edge of an 80-m tall cliff facing the sea, kicks a ball horizontally at a speed of 13.01 m/s. How far from the base of the cliff will the ball hit the sea water? Let be the initial vertical position of the ball, with positive position in the upward direction. The vertical displacement of the ball from the edge of the cliff to the seawater is: meters. The time it takes for the ball to reach the seawater is: t = seconds. The horizontal distance traveled by the ball is: meters.
- 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?Which of the following statement is/are true? a. The velocity of projectile motion in maximum height is zero. b. The velocity of an object in uniform circular motion is constant. c. During the flight of projectile motion, its horizontal velocity remains constant. d. The acceleration in free fall at the maximum height is zero.A 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.