What Are the Solutions to These 2D Motion Problems?

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The discussion revolves around solving various 2D motion problems from a homework assignment. Key topics include calculating the y-coordinate of a particle under constant acceleration, determining the velocity of a pebble after a specific displacement, and finding the magnitude of a cart's velocity at its maximum x-coordinate. Other problems involve projectile motion, centripetal acceleration on a Ferris wheel, and relative motion of raindrops observed from a moving train. The participant expresses urgency in needing assistance due to an upcoming major exam.
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please help me to solve these problems...

Homework Chapter 4 - 2D motion
MUAD GUTUB
Started: November 7, 2008 11:47 PM
Questions: 9

Instructions
1.
(Points: 1)
A particle starts from the origin at t=0 with a velocity of 5.00 j m/s and moves in the xy plane with constant acceleration (2.00 i+1.00 j) m/s2. When the particle x-coordinate is 27.7 m, what is its y coordinate? Give the answers to three significant figures.
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2.
(Points: 1)
A moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration a=(2.0 m/s2) i + (3.00 m/s2) j . At time t=0, the velocity is 5.00 (m/s) i. What is magnitude of its velocity when it has been displaced by 20.5 m parallel to x-axis? Give three significant figures.
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3.
(Points: 1)
A cart is propelled over an xy plane with an acceleration ax = - 2.00 m/s2 and ay = 1.00 m/s2 . Its velocity has components vox= 13.5 m/s and voy= 14.1 m/s. What is magnitude of cart’s velocity when it reaches its greatest x-coordinate? Give three significant figures.

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4.
(Points: 1)
A ball is shot from ground into the air. At a height of 8.7 m, its velocity is v=(2.0 i + 4.0 j), with i horizontal and j upward. What total horizontal distance the ball travel? Give two significant figures
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5.
(Points: 1)
A plane diving with constant speed at an angle of 54.6 degrees with the vertical (an angle of (90 - 54.6) below the horizontal x-axis), releases a projectile at an altitude of 800 m. The projectile hit the ground 4.0 s later. What is the angle of the projectile velocity with the x-axis when it hit the ground? Give three significant figures and to match the answer stored in the computer, please provide the answer with a negative sign - measured below the clockwise.
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6.
(Points: 1)
A woman rides a carnival Ferris wheel with radius 19.7 m, completing six revolutions about its horizontal axis every minute. What is magnitude of her centripetal acceleration at her highest point? Give the answer to three significant figures.
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7.
(Points: 1)
A particle moves horizontally in uniform circular motion over a xy plane. At one instant, it moves through the point at coordinates (2.00 m, 2.00 m) with a velocity of -6.75 i m/s and an acceleration of 16.2 j m/s2. What is y coordinates of the center of the circular path? Give three significant figures.
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8.
(Points: 1)
A person walk up a stalled 12.0-m long escalator in 60 s. When standing on the same escalator, now moving, the person is carried up in 40 s. How long would it take the person to walkup the moving escalator? Give the answer to two significant digits.
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9.
(Points: 1)
A train travels due south at 20.3 m/s (relative to the ground) in a rain that is blown towards the south by the wind. The path of each raindrop makes an angle of 60.0 degree with the vertical, as measured by an observer stationary on the ground. An observer on the train, however, sees the drop falls perfectly vertically. Determine the speed of the raindrop relative to the ground. Give three significant figures.
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