QCAA Physics Alternative Sequence Gravity and motion

A circular orbit requires a negative total energy and a launch parallel to the surface at a specific orbital velocity, which is less than the escape velocity.

An elliptical orbit requires the total energy of the system to be negative, meaning the launch velocity must be strictly less than the escape velocity.

While the trajectory is indeed a parabola, an object launched at or above escape velocity will overcome the planet's gravity and never return to land.

This is the initial vertical velocity, which is calculated using $v_0 \sin(\theta) = 38 \sin(42^\circ) \approx 25\ \text{m s}^{-1}$.

This value is incorrect and does not correspond to the proper trigonometric calculation for the horizontal component.

The horizontal component of the velocity cannot be greater than the total initial velocity of $38\ \text{m s}^{-1}$.

Incorrect. This value is obtained by multiplying Earth's escape velocity by $3/4$, incorrectly assuming escape velocity is proportional to $R/M$.

Incorrect. This value is obtained by multiplying Earth's escape velocity by $\sqrt{3/4}$, incorrectly assuming escape velocity is proportional to $\sqrt{R/M}$.

Incorrect. This value is obtained by multiplying Earth's escape velocity by $4/3$, incorrectly assuming escape velocity is proportional to $M/R$ instead of $\sqrt{M/R}$.

This defines gravitational field strength ($g = F/m$), which is a specific vector quantity at a point, rather than the concept of the field itself.

This is the definition of gravitational potential energy, which is the energy an object possesses due to its position, not the field.

This describes concepts related to gravitational potential and work done, rather than defining the region of space that constitutes the gravitational field.

This value is obtained by incorrectly using the tangent function ($\tan 30^\circ$) instead of the sine function to determine the vertical component of the initial velocity.

This result comes from mistakenly using the horizontal component of velocity ($v_0 \cos 30^\circ$) instead of the vertical component in the maximum height formula.

This calculates the maximum height for a projectile launched vertically upwards ($90^\circ$), completely ignoring the $30^\circ$ launch angle.

Incorrect. A force acting parallel to the surface is typically friction. The term "normal" in physics specifically means perpendicular.

Incorrect. While this is true for objects on a perfectly horizontal surface, the normal force acts at an angle on an inclined plane and horizontally if an object is pressed against a vertical wall.

Incorrect. Gravitational force always pulls straight down toward the center of the Earth, while the normal force pushes outward perpendicularly from the contact surface.

This assumes the orbital radius is inversely proportional to the square of the satellite's mass. However, orbital speed and radius are completely independent of the satellite's mass.

This incorrectly assumes the orbital radius is directly proportional to the satellite's mass. The mass of the orbiting object cancels out when equating gravitational and centripetal forces.

This incorrectly assumes the orbital radius is proportional to the square of the satellite's mass. A satellite's mass has no effect on its orbital radius for a given constant speed.

Equating gravitational force to centripetal force yields $v = \sqrt{GM/r}$, not $v \propto r^2$. This option incorrectly suggests velocity increases rapidly as the orbit gets larger.

While gravitational force is inversely proportional to the square of $r$ ($F_g \propto 1/r^2$), orbital velocity depends on the square root of the inverse of $r$.

This would mean velocity increases as the radius increases ($v \propto \sqrt{r}$). In reality, satellites further away experience weaker gravity and travel slower.

Incorrect. This value represents the acceleration of the object if there were no friction acting against it ($a = g \sin(35^\circ)$).

Incorrect. This result comes from incorrectly using cosine instead of sine to find the component of gravity parallel to the slope ($mg \cos(35^\circ)$).

Incorrect. This calculates the acceleration if friction were incorrectly added to the gravitational force, acting in the same direction down the slope rather than opposing the motion.