Projectile Motion of a Secondary Rocket in a Vertical Launch

[Toranc3]

Homework Statement

When it is 145 m above the ground, a rocket traveling vertically upward at a constant 8.50 m/s relative to the ground launches a secondary rocket at a speed of 12 m/s at an angle of 53 degrees above the horizontal, both quantities being measured by an astronaut sitting in the rocket. Air resistance is too small to worry about.

(a) Just as the secondary rocket is launched, what are the horizontal and vertical components of its velocity relative to (i) the astronaut sitting in the rocket and (ii) Mission Control on the ground?

(b) Find the initial speed and launch angle of the secondary rocket as measured by mission control.

(c) What maximum height above the ground does the secondary rocket reach?

Homework Equations

Vy=Vosin(θ)
Vx=Vocos(θ)

Vr2/e=Vr2/r1+Vr1/e

Vr2/e= velocity of rocket 2 relative to earth
Vr2/r1= velocity of rocket 2 relative to rocket 1
Vr1/e= velocity of rocket 1 relative to earth

The Attempt at a Solution

A)
i:
Vr2/r1-x= 12m/s*cos(53)=7.2217 m/s
Vr2/r1-y= 12m/s*sin(53)=9.5836 m/s

Vr2/e=vr2/r1 + vr1/e

ii: Vr2/e-y=vr2/r1-y + vr1/e-y
Vr2/3-y= 9.5836 m/s + 8.50m/s=18.0836m/s

Vr2/e-x=vr2/r1-x + vr1/e-x
vr2/e-x= 7.2217m/s + 0=7.2217m/s

Do I have part a right so far? thanks!

 

[Doc Al]

Do I have part a right so far? thanks!

Looks good to me!

 

[Toranc3]

Looks good to me!

Thank you Doctor!