A football is kicked at an angle 0, = 37.0° with a velocity of 20.0 m/s, as shown. Calculate (a) the maximum height, (b) the time of travel before the football hits the ground, (c) how far away it hits the ground,
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- Answer the following questions for projectile motion on level ground assuming negligible air resistance, with the initial angle being neither 0 nor 90 : (a) Is the acceleration ever zero? (b) Is the vector v ever parallel or antiparallel to the vector a? (c) Is the vector v ever perpendicular to the vector a? If so, where is this located?At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.Give an example of a trajectory in two or three dimensions caused by independent perpendicular motions.
- What is the y component of the vector (3i8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of those answersA motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.00-min trip, find (a) the total vector displacement, (b) the average speed, and (c) the average velocity. Let the positive x axis point east.Suppose that a particle begins its motion from the origin and meets the velocity (in m / s) given by: vx (t) = 2.50t vy (t) = 3.50√t. for t> 0 in seconds. Find the speed of the particle at t = 5.00 s What is the acceleration vector (in rectangular components) at t = 2.00 s ? Find the magnitude of the displacement between t = 0.00 s and t = 6.00 s
- 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. Vo - ( mis) 7 + 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/s?. The time needed to reach maximum height is t- S. The maximum height reached by the cannon ball is H= m.A ball is thrown from the edge of a cliff of height h=100 m with an initial horizontal velocity of Vy=10 m/s. a) How long does it take for the ball to reach the ground? b) How far has the ball traveled in the x direction when it hits the ground? c) What is the balls final velocity vector when it hits the ground? (Component form) d) What are the magnitude and direction of the ball's velocity when it hits the ground? (Polar form)A football is kicked at 25.0 m/s at an angle of 31.0° above the horizontal. Assume it starts 1.00 m above ground level. (Neglect any effects due to air resistance.) Describe the velocity vector of the ball in terms of its x- and y-components, vx and vy, respectively, when it is 6.00 m above ground level and still moving upward. Ux = m/s V = Describe the velocity vector of the ball in terms of its magnitude v and angle € above the horizon when it is 6.00 m above ground level and still moving upward. Vy = m/s 0 = m/s
- A projectile is launched at a height of h feet above the ground at an angle of e with the horizontal. The initial velocity is Vo feet per second, and the path of the projectile is modeled by the parametric equations (vo cos e )t and y= h+ (v, sin e)t – 1622 X = Write the parametric equations to model the path of a projectile launched from ground level (h = 0) at the given values of a and Vo. Use your equations to answer the following questions. 8= 10°, Vo = /0 feet per second • Determine the maximum height (to one decimal place). feet • Give the time the object reaches this height (to one decimal place). seconds • Give the approximate horizontal distance the objects is at this point (to one decimal place). feet • Determine the time the object will hit the ground after it is launched (to one decimal place). secondsAn ant undergoes three successive displacements: ?⃗1=3.00 m,20.0 degrees south of east ?⃗2=2.00 m,north ?⃗3=7.00 m,35.0 degrees west of south a) Carefully sketch and label the three displacements with their tails at the origin. Use a coordinate system in which the positive x-axis is east and the positive y-axis is north. b) Calculate the x-and y-components of each of the displacements. c) Use the results of part b) to calculate the distance between where the ant begins and where it ends. d) What fourth displacement (magnitude and direction) is necessary to return the ant to its initial position?Problem 4: An arrow is shot from a height of 1.95 m toward a cliff of height H. It is shot with a velocity of 28 m/s at an angle of 60° above the horizontal. It lands on the top edge of the cliff 3.99 s later. a) What is the height H of the cliff in meters b) what is the maximum heigh reached by the arrow along its tragectory in meters c) What is the arrow's speed just before hitting the cliff in m/s