Free fall Transitional Reasoning Practice

Questions

1. 1.

   During a structural testing experiment, a calibration sphere is launched vertically upward from the roof of a 40 m tall building with an initial speed $v_0$. The sphere ascends freely under gravity, momentarily comes to rest at its peak, and then falls past the edge of the roof to strike the ground at the base of the building with a speed of $3v_0$. Assuming air resistance is negligible and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the maximum height above the ground reached by the sphere?

   • A) 5 m
   • B) 50 m
   • C) 60 m
   • D) 45 m
2. 2.

   During a planetary exploration mission, an astronaut drops a scientific probe from rest from a height of 72 m above the airless surface of an unknown planet, recording that it takes exactly 6.0 s to reach the ground. Later, the astronaut launches the same probe vertically upward from the surface with an initial speed of 20 m/s. What maximum height above the surface does the probe reach during this launch?

   • A) 20 m
   • B) 25 m
   • C) 40 m
   • D) 50 m
3. 3.

   A stationary drone hovering at a constant altitude releases a supply package from rest. Exactly 2.0 s later, a second identical package is launched vertically downward from the same position so that both packages strike the ground at the exact same instant. If the first package takes 4.0 s to reach the ground, what must be the initial launch speed of the second package? (Neglect air resistance and take $g = 10\text{ m/s}^2$.)

   • A) 15 m/s
   • B) 20 m/s
   • C) 25 m/s
   • D) 30 m/s
4. 4.

   In an automated testing facility, a stationary drone hovering at an altitude of 80 m releases a calibration sphere from rest. At the exact same instant, a launcher on the ground fires a second sphere vertically upward. Optical tracking sensors record that the two spheres pass each other at an altitude of 60 m above the ground. Assuming air resistance is negligible and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what was the initial launch speed of the second sphere?

   • A) 20 m/s
   • B) 30 m/s
   • C) 40 m/s
   • D) 50 m/s
5. 5.

   During a field trial of an atmospheric probe, the device is launched vertically upward from ground level with an initial speed $v_0$. A stationary optical tracking sensor mounted on a tower at an altitude of 60 m detects the probe passing upward and then downward, recording an elapsed time of 4.0 s between the two detections. Assuming air resistance is negligible and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the launch speed $v_0$ of the probe?

   • A) 25 m/s
   • B) 30 m/s
   • C) 35 m/s
   • D) 40 m/s
6. 6.

   A weather balloon is ascending vertically at a constant speed of 5.0 m/s. When the balloon reaches an altitude of 30 m above the ground, a small sensor package is released. Assuming air resistance is negligible and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, how many seconds after its release does the sensor package strike the ground?

   • A) 2.0 s
   • B) 3.0 s
   • C) 4.5 s
   • D) 6.0 s
7. 7.

   In an evacuated vertical drop chamber, a spherical sensor is released from rest from the top of the chamber. Telemetry data reveals that during the first 2.0 s of free fall, the sensor traverses a vertical distance equal to $\frac{1}{9}$ of the chamber's total height. Assuming negligible air resistance and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the speed of the sensor at the moment it strikes the floor of the chamber?

   • A) 40 m/s
   • B) 60 m/s
   • C) 90 m/s
   • D) 180 m/s
8. 8.

   A sensor pod is released from rest at the top of an evacuated vertical drop shaft. An optical tracking system records the vertical distance traversed by the pod during two consecutive time intervals of equal duration $\Delta t$. The telemetry indicates that the pod covers 40 m more vertical distance during the second interval than during the first interval. Assuming air resistance is negligible and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the duration $\Delta t$ of each interval?

   • A) 1.0 s
   • B) 2.0 s
   • C) 2.8 s
   • D) 4.0 s
9. 9.

   During a vertical drop-tower experiment conducted in an evacuated chamber, an instrument package is released from rest from the top of the tower. High-speed timing sensors register that the package takes a duration $\tau$ to fall through the lower 75% of the tower's height. Assuming air resistance is negligible, what is the total time elapsed from the moment of release until the package reaches the bottom of the tower?

   • A) $2\tau$
   • B) $\frac{4}{3}\tau$
   • C) $\frac{2}{\sqrt{3}}\tau$
   • D) $4\tau$
10. 10.

    In an evacuated vertical drop tower, an autonomous sensor pod is released from rest to analyze one-dimensional free fall. The pod measures its average speed to be $v_1$ during the initial time interval of duration $T$, and its average speed to be $v_2$ during the immediately following time interval of duration $2T$. Assuming air resistance is negligible, what is the ratio $\frac{v_2}{v_1}$?

    • A) 4
    • B) 8
    • C) 3
    • D) 2
11. 11.

    An experimental sensor capsule is released from rest from a high platform inside an evacuated vertical test chamber. The capsule falls freely under gravity until it reaches the ground at the bottom of the chamber. What fraction of the total vertical fall distance is traversed by the capsule during the final third of its total descent time?

    • A) $\frac{1}{3}$
    • B) $\frac{4}{9}$
    • C) $\frac{5}{9}$
    • D) $\frac{2}{3}$
12. 12.

    In an atmospheric research facility, an experimental drop probe is released from rest inside a tall, evacuated vertical chamber. High-precision telemetry tracks the probe's descent under gravity alone. The data indicates that the vertical distance traversed by the probe during its fifth second of free fall is exactly equal to the total vertical distance it traversed during its first $k$ seconds of fall from rest. Assuming air resistance is negligible, what is the value of $k$?

    • A) 3
    • B) 2
    • C) 4
    • D) 5
13. 13.

    During a laboratory demonstration of one-dimensional motion, a small steel sphere is released from rest at a height $H$ above the ground inside an evacuated vertical drop chamber. Assuming air resistance is negligible, at what height above the ground is the sphere's instantaneous speed equal to its average speed for the entire fall?

    • A) $\frac{1}{4}H$
    • B) $\frac{3}{4}H$
    • C) $\frac{1}{2}H$
    • D) $\frac{\sqrt{2}}{2}H$
14. 14.

    In an evacuated vertical test chamber, an experimental probe is released from rest from a height $H$ above the floor. Telemetry data shows that the probe takes a time interval $t_1$ to fall through the upper half of the distance ($\frac{H}{2}$) and an interval $t_2$ to fall through the lower half ($\frac{H}{2}$). Assuming negligible air resistance, what is the ratio $\frac{t_1}{t_2}$?

    • A) $\sqrt{2} + 1$
    • B) $\sqrt{2} - 1$
    • C) $\sqrt{2}$
    • D) 1
15. 15.

    In a vacuum testing facility, two small calibration probes, P and Q, are dropped from rest from different heights above the floor to calibrate an optical impact sensor. Probe P is released from a height of 125 m at time $t = 0$, while probe Q is suspended at a height of 45 m directly above its own impact target. Assuming negligible air resistance and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, how many seconds after probe P must probe Q be released so that both probes hit the floor at the exact same instant?

    • A) 4.0 s
    • B) 3.0 s
    • C) 1.0 s
    • D) 2.0 s
16. 16.

    A solid steel sphere is released from rest inside an evacuated vertical drop tube. The sphere passes two optical timing gates separated by a vertical distance of 80 m, taking exactly 2.0 s to travel between them. Assuming negligible air resistance and taking $g = 10\text{ m/s}^2$, what is the vertical distance between the release point and the first timing gate?

    • A) 20 m
    • B) 35 m
    • C) 45 m
    • D) 80 m
17. 17.

    Two small sensor probes, X and Y, are released from rest from the same elevated platform in an evacuated vertical test shaft. Probe Y is released exactly 1.0 s after probe X. Assuming negligible air resistance and taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the vertical distance separating the two probes at the instant probe X reaches a downward speed of 30 m/s?

    • A) 10 m
    • B) 20 m
    • C) 25 m
    • D) 30 m
18. 18.

    A scientific drone hovering at a fixed altitude in a windless testing facility releases a small test capsule from rest. An acoustic ground sensor records that the capsule traverses a vertical distance of 35 m during its final second before hitting the ground. Assuming negligible air resistance and taking the acceleration due to gravity as $g = 10$ m/s², what was the initial altitude of the drone above the ground?

    • A) 45 m
    • B) 60 m
    • C) 80 m
    • D) 125 m
19. 19.

    In a physics laboratory, a sensor records the motion of a steel sphere dropped from rest inside an evacuated vertical drop tower. The sphere reaches a speed $v$ after falling a vertical distance $d$ from its release point. Assuming negligible air resistance, what additional vertical distance must the sphere fall from this point to reach a speed of $3v$?

    • A) $2d$
    • B) $4d$
    • C) $8d$
    • D) $9d$
20. 20.

    During an experiment investigating one-dimensional free fall, a steel sphere is released from rest in an evacuated vertical chamber where air resistance is negligible. A high-speed strobe camera records the vertical position of the sphere at regular time intervals of $\Delta t$. If the vertical distance traversed by the sphere from release to the first flash is $h_1$, and the distance traversed between the first flash and the second flash is $h_2$, what is the ratio $\frac{h_2}{h_1}$?

    • A) 2
    • B) 3
    • C) 4
    • D) 5

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