Horizontal launch Transitional Reasoning Download PDF

Questions

1. 1.

   During a safety test on an outdoor training course, a projectile is launched horizontally from the top edge of a uniform slope inclined downward at an angle of 37° below the horizontal. The projectile is fired with an initial speed of 20 m/s and moves freely under gravity until it impacts the slope. Assuming air resistance is negligible, taking the acceleration due to gravity as 10 m/s², and using $\sin 37^\circ \approx 0.6$ and $\cos 37^\circ \approx 0.8$, what is the straight-line distance along the slope from the launch point to the landing point?

   • A) 45 m
   • B) 60 m
   • C) 75 m
   • D) 90 m
2. 2.

   During a laboratory trial, an automated launcher projects a small sphere horizontally from an elevated track. Two optical sensors positioned along its trajectory record that the sphere takes 1.0 s to travel between them, descending a vertical distance of 15 m while covering a horizontal distance of 12 m. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the total horizontal distance traveled by the sphere from the launch point to the second sensor?

   • A) 24 m
   • B) 18 m
   • C) 30 m
   • D) 36 m
3. 3.

   During a field test of an autonomous emergency delivery system, a payload is launched horizontally from an elevated cliff over flat terrain. Telemetry records that at a certain moment during flight, the payload has descended a vertical distance of 45 m while covering a horizontal distance of 90 m. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the angle between the payload's velocity vector and the horizontal at that moment?

   • A) 45°
   • B) 30°
   • C) 60°
   • D) 37°
4. 4.

   A student investigates horizontal projectile motion in a physics laboratory using an elevated launcher fixed at an unknown height above a flat floor. In the first trial, a steel sphere is launched horizontally with an initial speed $v_1$ and lands at a horizontal distance of 4.0 m from the base of the launcher. In a second trial from the same height, the sphere is launched in the same direction with its initial speed increased by 2.5 m/s, landing at a horizontal distance of 6.0 m. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the height of the launcher above the floor?

   • A) 1.6 m
   • B) 2.4 m
   • C) 3.2 m
   • D) 6.4 m
5. 5.

   An automated transport cart on a flat warehouse floor moves at a constant speed of 2.5 m/s directly away from the base of a 7.2 m high loading platform. At the instant the cart is 4.2 m from the base of the platform, a package is launched horizontally from the platform edge in the direction of the cart's motion. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what initial horizontal speed must the package have to land directly on the cart?

   • A) 1.0 m/s
   • B) 3.5 m/s
   • C) 6.0 m/s
   • D) 8.5 m/s
6. 6.

   A projectile is launched horizontally with an initial speed $v_0$ in an environment where air resistance is negligible. At the moment the projectile has traveled a horizontal distance $d$, its instantaneous velocity vector is directed at $37^\circ$ below the horizontal. As the projectile continues along its path, its velocity vector reaches an angle of $53^\circ$ below the horizontal. In terms of $d$, what additional horizontal distance does the projectile travel between these two points? (Take $\tan 37^\circ \approx \frac{3}{4}$ and $\tan 53^\circ \approx \frac{4}{3}$.)

   • A) $\frac{7}{16}d$
   • B) $\frac{1}{2}d$
   • C) $\frac{7}{12}d$
   • D) $\frac{7}{9}d$
7. 7.

   A projectile is launched horizontally from an elevated point with an initial speed $v_0$. At a particular point along its trajectory, the magnitude of the projectile's vertical displacement from the launch position equals its horizontal displacement. Assuming air resistance is negligible, what is the ratio of the projectile's kinetic energy at this point to its initial kinetic energy?

   • A) 2
   • B) 4
   • C) 5
   • D) 8
8. 8.

   A robotic mechanism launches a small puck horizontally from a platform of height 1.8 m above a level floor. A vertical barrier of height 1.0 m stands on the floor at a horizontal distance of 2.4 m from the platform edge. Assuming negligible air resistance and taking the acceleration due to gravity as 10 m/s², what is the minimum launch speed needed for the puck to clear the top of the barrier?

   • A) 4.0 m/s
   • B) 6.0 m/s
   • C) 8.0 m/s
   • D) 12.0 m/s
9. 9.

   A search-and-rescue airplane flying horizontally at an altitude of 180 m above level ground releases an emergency supply crate. Ground tracking instruments determine that the crate strikes the ground with its velocity vector directed at an angle of 45° below the horizontal. Assuming negligible air resistance and taking the acceleration due to gravity as 10 m/s², what was the horizontal speed of the airplane at the moment of release?

   • A) 30 m/s
   • B) 60 m/s
   • C) 90 m/s
   • D) 120 m/s
10. 10.

    In an investigation of two-dimensional motion, a robotic launcher rolls a small steel ball horizontally off a laboratory bench that is 0.80 m above a level floor. The ball lands on the floor at a horizontal distance of 1.20 m from the edge of the bench. Assuming negligible air resistance and taking the acceleration due to gravity as 10 m/s², what is the magnitude of the ball's velocity just before it strikes the floor?

    • A) 5.0 m/s
    • B) 4.0 m/s
    • C) 3.0 m/s
    • D) 7.0 m/s
11. 11.

    In a physics laboratory investigation, an automated mechanism launches two identical metal spheres, X and Y, horizontally from different heights above a flat floor. Sphere X is launched with an initial horizontal speed $v$ from a height $h$, while sphere Y is launched with an initial horizontal speed $2v$ from a height $4h$. Neglecting air resistance, what is the ratio of the horizontal distance traveled by sphere Y to that traveled by sphere X?

    • A) 1
    • B) 2
    • C) 4
    • D) 8