Suppose the position of a particle at time t (assume time is in seconds_ is give

Question

Suppose the position of a particle at time t (assume time is in seconds_ is given by the vector function: r(t)=. (a). at what time does the particle pass through the xy-plane? (b). What is the speed of the particle at the time you found in (a)? For this question you must provide an exact answer, but you do not need to simplify the radical. :D

Explanation / Answer

r(t) = (t^4,t^3,t-7) => x(t)=t^4 y(t)=t^3 z(t)=t-7 the particle passes through x-y plane when z=0 => 0=t-7 => t=7 and hence x=7^4 = 2401 y= 7^3 = 343 Vx(speed in x direction) = dx/dt = 4t^3 = 1372 Vy = dy/dt = 3t^2 = 147 Vz = dz/dt = 1 speed of the particle = sqrt(Vx^2 +Vy^2 + Vz^2) => v = sqrt ( 1372^2 + 147^2 + 1) v = 1379.852 (aprrox)

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