Horizontal launch Transitional Reasoning Practice

Questions

1. 1.

   During an aerial delivery test over flat terrain, an autonomous drone flying horizontally at an altitude of 180 m drops an instrumentation capsule. Optical tracking sensors record that after the capsule falls vertically through a distance of 45 m, its instantaneous speed is 50 m/s. 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 capsule from release to ground impact?

   • A) 120 m
   • B) 180 m
   • C) 240 m
   • D) 300 m
2. 2.

   An environmental survey drone releases an instrument canister horizontally above a flat valley floor to record atmospheric data. Telemetry shows that during the final 1.0 s of flight before ground impact, the canister falls a vertical distance of 35 m under gravity. If the canister travels a total horizontal distance of 60 m from its release point to the landing site, what was the horizontal speed of the drone at the moment of release? (Neglect air resistance and take g = 10 m/s².)

   • A) 10 m/s
   • B) 12 m/s
   • C) 15 m/s
   • D) 20 m/s
3. 3.

   During a trajectory tracking experiment, a test capsule is launched horizontally from an elevated platform. Optical tracking stations record that the capsule takes 2.0 s to travel between two points, A and B, along its flight path, covering a horizontal distance of 40 m and dropping a vertical distance of 80 m during this interval. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, what is the straight-line distance from the launch platform to point A?

   • A) 65 m
   • B) 75 m
   • C) 85 m
   • D) 105 m
4. 4.

   During a trajectory evaluation test inside an enclosed research chamber, a projectile is launched horizontally from an elevated fixture with an initial kinetic energy of 180 J. High-speed optical tracking records the flight until the instant the velocity vector points at an angle of $60^\circ$ below the horizontal. Assuming air resistance is negligible, what is the work done by gravity on the projectile from launch to this recorded instant?

   • A) 180 J
   • B) 360 J
   • C) 720 J
   • D) 540 J
5. 5.

   During a trajectory analysis inside a test chamber, an instrumentation capsule is launched horizontally from an elevated platform. High-speed sensors record that after the capsule falls vertically through a distance of 20 m, its velocity vector is directed at 45° below the horizontal. If the capsule continues its flight and strikes the ground with its velocity vector directed at 60° below the horizontal, from what height above the ground was it launched?

   • A) 30 m
   • B) 40 m
   • C) 50 m
   • D) 60 m
6. 6.

   In an automated ballistic interception test, a target drone is released from rest from a height of 125 m above the ground. At the exact same instant, a tracking projectile is launched horizontally toward the drone's vertical line of descent from a platform located at the same height of 125 m and at a horizontal distance of 75 m away. If the tracking projectile has an initial horizontal speed of 25 m/s, at what height above the ground does the projectile intercept the falling drone? (Neglect air resistance and take g = 10 m/s².)

   • A) 80 m
   • B) 45 m
   • C) 35 m
   • D) 50 m
7. 7.

   During a trajectory trial in a testing facility, two small tracking beacons are launched horizontally in the same direction from the edge of an elevated cliff. Beacon 1 is launched with an initial speed of 12 m/s, and Beacon 2 is launched 1.0 s later from the same position with an initial speed of 18 m/s. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, what is the vertical separation between the two beacons at the instant they reach the same horizontal distance from the cliff?

   • A) 15 m
   • B) 20 m
   • C) 25 m
   • D) 35 m
8. 8.

   An automated sorting system slides packaged items horizontally off the flat edge of an inspection table elevated 1.8 m above the floor. To be collected properly, each package must land inside a rectangular bin resting on the floor, whose nearest edge is 2.4 m and farthest edge is 3.6 m from the base of the table. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what range of initial launch speeds will ensure that a package lands inside the bin?

   • A) Between 2.0 m/s and 3.0 m/s
   • B) Between 3.0 m/s and 4.5 m/s
   • C) Between 4.8 m/s and 7.2 m/s
   • D) Between 4.0 m/s and 6.0 m/s
9. 9.

   During an automated interception trial, a projectile is launched horizontally with an initial speed of 12 m/s from the edge of a flat platform 45 m above the ground. At the same instant, a target vehicle located at a horizontal distance of 60 m from the base of the platform begins moving toward the platform along a straight track at a constant speed $u$. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what must the speed $u$ of the target vehicle be for the projectile to strike it upon reaching the ground?

   • A) 4.0 m/s
   • B) 8.0 m/s
   • C) 12.0 m/s
   • D) 20.0 m/s
10. 10.

    During a field test on a terrain simulator, a survey vehicle launches a small sensor horizontally from the crest of a uniform slope with an initial speed of 20 m/s. The hillside descends steadily at an inclination such that it drops 3.0 m vertically for every 4.0 m of horizontal distance. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the straight-line distance along the slope from the launch crest to the landing point?

    • A) 60 m
    • B) 75 m
    • C) 80 m
    • D) 100 m
11. 11.

    During a laboratory demonstration, two small test spheres are launched simultaneously in opposite horizontal directions from the same elevated point with initial speeds of 3.0 m/s and 12.0 m/s, respectively. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the straight-line distance between the two spheres at the instant their velocity vectors become mutually perpendicular?

    • A) 5.4 m
    • B) 7.2 m
    • C) 9.0 m
    • D) 13.5 m
12. 12.

    During a ballistics trajectory experiment in a testing facility, a small sphere is launched horizontally from an elevated platform. Two vertical optical sensors placed at horizontal distances of 40 m and 80 m from the launch edge record that the sphere drops an additional vertical distance of 60 m between the first and second sensor planes. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the initial horizontal speed of the sphere?

    • A) 20 m/s
    • B) 15 m/s
    • C) 10 m/s
    • D) 40 m/s
13. 13.

    During an environmental monitoring test, a meteorological probe is launched horizontally from an elevated cliff with an initial speed of 8.0 m/s. Telemetry data confirms that the probe moves under gravity alone and strikes the ground 3.0 s after release. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what is the magnitude of the probe's average velocity vector over the entire flight?

    • A) 8.0 m/s
    • B) 23 m/s
    • C) 31 m/s
    • D) 17 m/s
14. 14.

    An automated container crane moving horizontally along an overhead track at a height of 80 m above a terminal floor must release a cargo container to land on a designated target. At the release point, a sensor measures the straight-line distance between the crane and the target to be 100 m. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what constant horizontal speed must the crane have at the moment of release?

    • A) 15 m/s
    • B) 20 m/s
    • C) 25 m/s
    • D) 30 m/s
15. 15.

    A ballistics tracking system monitors a projectile launched horizontally from an elevated platform into a testing chamber. At a specific telemetry point along the trajectory, sensors record that the magnitude of the projectile's vertical velocity component is three times its horizontal velocity component. Neglecting air resistance, what is the ratio of the projectile's vertical displacement from the launch position to its horizontal displacement from the launch position at this instant?

    • A) $\frac{3}{2}$
    • B) 3
    • C) $\frac{9}{2}$
    • D) $\frac{2}{3}$
16. 16.

    During a field test, an autonomous rover drives horizontally off a flat ledge of height 45 m to clear an obstacle. A vertical security wall of height 25 m stands at a horizontal distance of 60 m from the base of the ledge. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what is the minimum initial horizontal speed the rover must have to pass above the wall?

    • A) 15 m/s
    • B) 20 m/s
    • C) 30 m/s
    • D) 40 m/s
17. 17.

    During an automated sorting calibration test, two packages, P and Q, are projected horizontally from separate conveyor platforms above a flat warehouse floor. Package P is launched from a height $h$ with an initial horizontal speed $2v$ and lands at a horizontal range $d$ from its launch platform. If Package Q is launched with an initial horizontal speed $v$ and lands at the same horizontal range $d$, what is the launch height of Package Q in terms of $h$?

    • A) $2h$
    • B) $4h$
    • C) $\sqrt{2}h$
    • D) $8h$
18. 18.

    During a high-altitude emergency drill across a flat testing ground, a rescue projectile is launched horizontally from the edge of a cliff of height $h$. Telemetry recorded right before impact shows that the projectile's velocity vector is directed at an angle of $45^\circ$ below the horizontal. Assuming air resistance is negligible, what is the total horizontal distance traveled by the projectile in terms of $h$?

    • A) $2h$
    • B) $h$
    • C) $\sqrt{2}h$
    • D) $\frac{h}{2}$
19. 19.

    A prototype delivery capsule is launched horizontally from an elevated testing ledge with an initial speed of 15 m/s. Telemetry sensors record that the capsule strikes the ground with a total resultant speed of 25 m/s. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², from what height above the ground was the capsule launched?

    • A) 20 m
    • B) 31.25 m
    • C) 11.25 m
    • D) 40 m
20. 20.

    An automated surveying drone flying horizontally at a constant speed of 24 m/s at an altitude of 45 m above a flat plain releases a sensor package. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what horizontal distance does the package cover between its release and ground impact?

    • A) 72 m
    • B) 108 m
    • C) 48 m
    • D) 144 m

Answers and step-by-step solutions appear after you finish the test.