When it is 152 m above the ground, a rocket traveling vertically upward at a constant 9.50 m/s relative to the ground launches a secondary rocket at a speed of 12.4 m/s at an angle of 50.0 degrees above the horizontal, both quantities being measured by an observer sitting in the rocket. Air resistance should be ignored.
Just as the secondary rocket is launched, what are the horizontal and vertical components of its velocity relative to Mission Control on the ground?
well, if the 12.4m/s per second was measured by a ground observer, then that is the actual velocity.
vertical: 12.4sin50
horizontal: 12.4cos50
Normally, I would have assumed the 12.4m/s was relative to the launching rocket, so that the actual velocity would be added to the rocket. Such is life.
To determine the horizontal and vertical components of the velocity of the secondary rocket relative to Mission Control on the ground, we need to consider the rocket's launch velocity relative to the observer sitting in the rocket and the vertical velocity of the rocket.
The rocket's launch velocity relative to the observer in the rocket is 12.4 m/s at an angle of 50.0 degrees above the horizontal. From this, we can calculate the horizontal and vertical components of this velocity.
The horizontal component of velocity (Vx) can be calculated using the formula:
Vx = V * cos(θ),
where V is the magnitude of the launch velocity (12.4 m/s) and θ is the angle of 50.0 degrees.
Vx = 12.4 m/s * cos(50.0 degrees)
Calculating this, we find:
Vx = 12.4 m/s * 0.6428 ≈ 7.97 m/s (rounded to two decimal places).
Therefore, the horizontal component of the velocity of the secondary rocket relative to Mission Control on the ground is approximately 7.97 m/s.
The vertical component of velocity (Vy) can be calculated using the formula:
Vy = V * sin(θ),
where V is the magnitude of the launch velocity (12.4 m/s) and θ is the angle of 50.0 degrees.
Vy = 12.4 m/s * sin(50.0 degrees)
Calculating this, we find:
Vy = 12.4 m/s * 0.766 ≈ 9.49 m/s (rounded to two decimal places).
Therefore, the vertical component of the velocity of the secondary rocket relative to Mission Control on the ground is approximately 9.49 m/s.
Hence, the horizontal and vertical components of the velocity of the secondary rocket relative to Mission Control on the ground are approximately 7.97 m/s and 9.49 m/s, respectively.