A planet has an unusual mass distribution. at a location near its surface, g is

Question

A planet has an unusual mass distribution. at a location near its surface, g is given by g=2ax-15az. Where that x-axis is due east and the y-axis is due north. The z-axis is up. There is also a constant electric field of value E=3ay+az. A small, spherical drone entering this space has an initial velocity of v0=2ax+4ay+2az and an initial position of r0=ax-2ay+4az. the drone has a mass of 2.0kg and an electric charge of 2.0C. there is no wind resistance. find a,V,r of the drone as a function of tine t and in terms of ax,ay,az. Find the magnitudes of a,V,r.

Explanation / Answer

Force on drone due to gravity Fg=m(g)=2(2ax-15az)=4ax-30az force on drone due to electric field Fe=qE=2(3ay+az)=6ay-2az total force on drone F=Fg+Fe=4ax-30az+6ay-2az=4ax+6ay-32az acceleration a = F/m = (4az+6ay-32z)/2 = 2ax+3ay-16az velocity v= v0 + a*t =2ax+4ay+2az + (2ax+3ay-16az)*t v = (2+zt)ax + (4+3t)ay + (2-16t)az displacement r = r0 + v0*t + 0.5*a*t^2 = ax-2ay+4az + (2ax+4ay+2az)*t + 0.5*(2ax+3ay-16az)*t^2 = (1+2t+t^2)ax + (-2+4t+1.5t^2)ay + (4+2t-8t^2)az

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.