A rocket starts from rest and moves upward from the surface of the earth. For the first 10.0 s of its motion, the vertical acceleration of the rocket is given by a, = (3.00 m/s) t, where the +y- direction is upward.

The acceleration of a particle is a = (5.00 i - 7.00 j) m/s^2. At t = 0, the particle leavesthe origin with an initial velocity v0 = (4.00 i + 1.00 j) m/s. (a) What is the y-coordinate of the particle when its x-coordinate reaches 2.00 m? (b) What are the magnitude and direction of the particle's velocity when its x-coordinate reaches 2.00 m? Draw this velocity vector.

A rocket starts from rest and moves upward from thesurface of the earth. For the first 10.0 s of its motion, the vertical accelerationof the rocket is given by ay = 12.80 m/s32t, where the+y-direction is upward. What is the height of the rocket above the surface of the earth at t = 10.0 s?

A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 2.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is  = (25.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax =   ay =   (b) What is the direction of its acceleration with respect to unit vector î? Draw coordinate axes on a separate piece of paper, and then add the acceleration vector with its tail at the origin. Write the numerical values for the x and y components and then use this drawing to determine the angle.° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 28.0 s? x =  m y =  m In what direction is it moving? ° counterclockwise from the +x-axis

A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is (-22.5 î + 20.2 ĵ ) m/s2. For that instant, (a) sketch a vectordiagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.

​Suppose the position vector for a particle is given as a function of time by , with x(t) = at + b and y(t) =ct2 + d, where a = 1.00 m/s, b = 1.00 m, c= 0.125 m/s2, and d = 1.00 m. (a) Calculate the average velocity during the time interval from t = 1.00 s to t = 4.00 s. (b) Determine the velocity and the speed at t = 3.00 s. (c) Determine the acceleration at t = 3.00 s.

A puma (aka cougar or mountain lion) is one of the best jumpers among all animals. It can jump to a height of 12.0 feet high when it leaves the ground at an initial angle of 45°. What is the initial speed (in m/s) of the puma as it leaves the ground?

Dock diving is great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.02 m/s at an angle of 25.0° with respect to the surface of the water. Sheba begins at a height of 0.840 m above the surface of the water. What is her total time of flight up until the instant before she hits the water? Express your answer in seconds.

A fish swimming in a horizontal plane has velocity V₁ = (4.00 i + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r = (16.01- 3.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (15.01 - 1.00 j) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 m/s2 ay = (b) What is the direction of its acceleration with respect to unit vector î? counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 24.0 s? x = y = m In what direction is it moving? counterclockwise from the +x-axis

A particle's position is given by  z(t) = −(7.30 m/s2)t2  for  t ≥ 0.  (Express your answer in vector form.) (a) Find the particle's velocity at  t = 2.50 s  and  t = 3.25 s. (b) What is the particle's average velocity during the time interval from  t = 2.50 s  to  t = 3.25 s?