The position of a particle moving in the xy plane axis is given by r(t) = (3.00t

Question

The position of a particle moving in the xy plane axis is given by r(t) = (3.00t^3 -9.00t)$+(3.00 -4.00t^4)^$j, where r(t) is in m and tis ins. a. Determine the particle's position, velocity, and acceleration at t = 3.0 s in unit vector notation. b. What is the magnitude and direction of the particle's velocity at t = 3.0 s? 2. The velocity of a particle moving in the xy plane is given by nu(t) = (6.0t - 4.0t^2)$1 + 9.0^$j with nu(t) in m/s and t (>0) in s. a. What is the acceleration when t = 1.0 s? b. When is the acceleration zero? c. Can the velocity ever be zero? d. When does the speed equal 10 m/s? 3. A certain airplane has a speed of 350.0 km/h and is diving at an angle of 30.0degree below the horizontal when the pilot releases a radar decoy. The horizontal distance between the release point and the point where the decay strikes the ground is 700m. (Neglect air resistance.) a. How high was the plane when the decoy was released? b. How long was the decoy in the air?

Explanation / Answer

1. at t=3 ; position(r)= 54 i -321 j

velocity= dr/dt = (9t2-9) i - 16t3 j

at t=3; velocity(v)= 72i -432 j

acceleration(a)= dv/dt = (18t) i -(48t2 )j

at t=3; a= 54i -432 j

b. magnitude of v= sqrt(722 + 4322) =437.959 ms-1

tan(x)= <<j component>> / <<icomponent>> = -432/72

angle(x)= 80.538 clockwisely

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