Questions: The planet Tralfamador is a planet of mass M and Radius R, and very t

Question

Questions: The planet Tralfamador is a planet of mass Mand Radius R, and very thin atmosphere (neglect airresistance). A magnetic rail gun has been mounted on the surface ofTralfamador at the North pole. A projectile of mass m isfired from the magnetic rail gun with an unknown speedvo at an unknown angle with repect to thelock horizontal. The projectile is observed to rise to a maximumheight above the surface of 1/4 Radius. At this maximum height theprojectile has a speed of 75.0 m/s

1) If M = 1.5 x 1020 kg( so that GM =1.0 x1010 Nm2/kg) and R = 200 km, findvo in m/s.

2. Find the launch angle

Explanation / Answer

    Since the height is significant withrespect to the radius of the planet,     g = GM/R2     So, the loss of vertical component ofkinetic energy, ie. 1/2*m*(v0sin)2 =GMm*[1/R - 1/(R+h)]      Now, v0cos, ie. thehorizontal component of velocity remains unaltered as no force actsin that direction.     So, v0cos = speed at maxheight = 75 m/s     now, v0sin =[2*4GM/5R] {taking h=R/4}     So, v0= ?      use cos2 +sin2 = 1     Then using v0cos = 75 m/syou will get .     So, the loss of vertical component ofkinetic energy, ie. 1/2*m*(v0sin)2 =GMm*[1/R - 1/(R+h)]      Now, v0cos, ie. thehorizontal component of velocity remains unaltered as no force actsin that direction.     So, v0cos = speed at maxheight = 75 m/s     now, v0sin =[2*4GM/5R] {taking h=R/4}     So, v0= ?      use cos2 +sin2 = 1     Then using v0cos = 75 m/syou will get .

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

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