The coordinates of an object as a function of time are given by X= -0.31 t2 + 7.2 t + 28, and Y= 0.22 t2-9.1 t + 30 Find the position vector, velocity, and acceleration at t=15 seconds

Taking north to be the positive y direction and east to be the positive x direction, a particle's position is given byr(t) = (20.2m/s)t^i+(5.15 m/s2)t2^jAt what time, in seconds, is the particle traveling exactly northeast?

A mountain lion jumps to a height of 2.80 m when leaving the ground at an angle of 43.1°. What is its initial speed (in m/s) as it leaves the ground?  m/s

The best leaper in the animal kingdom is the puma, which can jump to a height of 12.7 ft when leaving the ground at an angle of 50°. With what speed, in SI units, must the animal leave the ground to reach that height?

A particle initially located at the origin has an acceleration of a = 1.00ĵ m/s2 and an initial velocity of ₁ = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + t²ĵ) m (b) Find the velocity of the particle at any time t. Î+ tĵ) m/s (c) Find the coordinates of the particle at t = 4.00 s. X = y = m m (d) Find the speed of the particle at t = 4.00 s. m/s

At an air show, a jet plane has velocity components vx =695km/h and vy  =415km/h  at time 4.35 s and vx =938km/h and vy =365km/h at time 7.52 s.   Please answer A,B,C,D Thank you.

Chapter 02, Problem 10 In reaching her destination, a backpacker walks with an average velocity of 1.26 m/s, due west. This average velocity results, because she hikes for 6.62 km with an average velocity of 2.54 m/s due west, turns around, and hikes with an average velocity of 0.381 m/s due east. How far east did she walk (in kilometers)? dw VE West East dɛ Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show Work

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A runner, jogging along a straight-line path, starts at a position 60.0 m east of a milestone marker and heads west. After a short time interval he is 15.7 m west of the mile marker. Choose east to be the positive x-direction. What is the runner’s displacement from his starting point? Enter a positive value if the displacement is toward east of the milestone and a negative value if the displacement is toward west of the milestone.

Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 3. a(t) = 8i + 4k v(0) = 5j, r(0) = 0 v(t) = r(t) = r(3) =