A small metal ball is kicked from the edge of a cliff. Its X- and y-coordinates as functions of time are given by X = 18.5t and y = 3.84t 4.90t2, where X and y are in meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors i and 5. (Give the answer in terms of t.) Q l'= m By taking derivatives, do the following. (b) Obtain the expression for the velocity vector 3 as a function of time (in m/s). (Give the answers in terms oft.) _, v = m/s (c) Obtain the expression for the acceleration vector 3 as a function of time (in m/sz). .. a = m/s2 (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 3.03 5. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/sz.) ., r = m .. v = m/s _., a = m/s2 Submit Answer 2. DETAILS MY NOTES ASK YOUR TEACHER The vector position of a particle varies in time according to the expression r = 7.20 i - 8.00t j where I is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) V = m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) a = m/s2 (c) Calculate the particle's position and velocity at t = 4.00 s. T= m m/sA particle initially located at the origin has an acceleration ofi> = 2.00j m/s2 and an initial velocity of Vi = 6.00i m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( ti+ t23)m (b) Find the velocity of the particle at any time t. ( i + t 3) m/s (c) Find the coordinates of the particle at t = 9.00 s. x = m y: m (d) Find the speed of the particle at t = 9.00 5. m/s A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.90 m/s at an angle of 23.0 below the horizontal. It strikes the ground 6.00 5 later. (a) How far horizontally from the base of the building does the ball strike the ground? ITl {b2 Find the height from which the ball was thrown. m (c) How long does it take the ball to reach a point 10.0 m below the level of launching? s To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 320 m/s at 57.0 above the horizontal. It explodes on the mountainside 40.0 s after ring. What are the x and y coordinates of the shell where it explodes, relative to its ring point? X= m y= m A 2.20 kg wooden block is tied to a rope and spun in a circular path of radius 1.18 m. The block obtains a maximum speed of 12.0 m/s. What is the magnitude of the maximum radial acceleration (in m/sz) of the block? m/s2 A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. when kicked, the ball leaves the ground with a speed of 23.4 m/s at an angle of 52.0 to the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.) m (b) Does the ball approach the crossbar while still rising or while falling? O rising O falling A small, spring-loaded cannon launches a golf ball from level ground with an initial speed v, at an angle 9i with the horizontal. The golf ball lands a horizontal distance R from its launch point. The highest point the golf ball reaches during its ight is a distance 112 above the ground. In terms of R and 9, nd the following. (You may ignore air resistance.) (a) the time interval during which the golf ball is in motion t= (b) the golf ball's speed at the peak of its path v: (c) the initial vertical component of its velocity vyi = (d) its initial speed Vi: (e) the angle 9i (Assume 9i is in radians. Do not include units in your answer.) 9,. = rad (f) Suppose the golf ball is launched at the same initial speed found in (d) but at the angle appropriate for reaching the greatest height that it can. Find this height. h max (9) Suppose the golf ball is launched at the same initial speed but at the angle for greatest possible range. Find this maximum horizontal range. Xmax An astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 700 km above the Earth's surface, where the free-fall acceleration is 8.21 m/sz. Take the radius of the Earth as 6400 km. Determine the speed of the satellite. m/s Determine the time interval required to complete one orbit around the Earth, which is the period of the satellite. min This figure (la| = 18.5 m/s2) represents the total acceleration of a particle moving clockwise in a circle of radius r = 4.20 m at a certain instant of time. 30.00 (a) For that instant, find the radial acceleration of the particle. m/s2 (toward the center) (b) For that instant, find the speed of the particle. m/s (c) For that instant, find its tangential acceleration. m/s2 (in the direction of the motion)