Projectile motion Transitional Reasoning Download PDF

Questions

1. 1.

   During a ballistics trial across flat horizontal ground, a test projectile is launched from ground level with an initial speed of 40 m/s at an angle of $53^\circ$ above the horizontal. Telemetry tracks the flight of the projectile until its velocity vector becomes perpendicular to its initial launch velocity vector. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, how many seconds after launch does this occur?

   • A) 3.2 s
   • B) 4.0 s
   • C) 5.0 s
   • D) 6.4 s
2. 2.

   During a ballistics demonstration over level ground, two identical projectiles are fired from the same launch point with equal initial speeds at complementary launch angles. Telemetry records that projectile 1 remains in the air for 2.0 s, while projectile 2 remains in the air for 8.0 s before both land at the same impact location. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, what is the horizontal range from the launch point to their landing point?

   • A) 40 m
   • B) 100 m
   • C) 160 m
   • D) 80 m
3. 3.

   During a ballistics trial across flat horizontal ground, a projectile is launched at an angle into the air. High-speed tracking records that the projectile's velocity vector is inclined at $45^\circ$ above the horizontal when it ascends through an altitude of 15 m, and it reaches the peak of its trajectory exactly 1.0 s later. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the total horizontal range of the projectile when it lands back on the ground?

   • A) 30 m
   • B) 40 m
   • C) 50 m
   • D) 60 m
4. 4.

   During a field trial across flat horizontal ground, an automated launcher fires a test projectile at an angle into the air. Onboard telemetry records that while ascending at an altitude of 25 m above the ground, the projectile has a speed of 25 m/s directed at an angle of $53^\circ$ above the horizontal. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, what is the total horizontal range of the projectile when it lands back on the ground?

   • A) 60 m
   • B) 75 m
   • C) 90 m
   • D) 120 m
5. 5.

   During a field demonstration, an automated launcher fires a test projectile from ground level across flat terrain. The projectile just clears the top of a 40 m tall observation tower located at a horizontal distance of 40 m from the launch site, and it lands back on the ground at a total horizontal range of 120 m. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the maximum height reached by the projectile during its flight?

   • A) 45 m
   • B) 50 m
   • C) 54 m
   • D) 60 m
6. 6.

   During a field test, an automated research probe is launched horizontally from the edge of an observation cliff with an initial speed of 15 m/s. Telemetry records show that the probe strikes the flat ground below with an impact speed of 25 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the horizontal distance from the base of the cliff to the impact point?

   • A) 15 m
   • B) 20 m
   • C) 30 m
   • D) 45 m
7. 7.

   During a field test of an autonomous surveying rocket, the vehicle is launched from ground level across flat, horizontal terrain. Telemetry data shows that the rocket reaches its maximum height 4.0 s after launch, and its speed at this peak point is 15 m/s. Assuming air resistance is negligible and taking $g = 10\text{ m/s}^2$, what is the straight-line distance from the launch point to the rocket at its maximum height?

   • A) 60 m
   • B) 80 m
   • C) 120 m
   • D) 100 m
8. 8.

   During a field test of an autonomous surveying system, a small sensor module is launched from an elevated observation platform at an angle of $37^\circ$ above the horizontal. Telemetry indicates that the module remains airborne for 4.0 s before striking the horizontal ground at a horizontal distance of 64 m from the launch platform. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, $\cos 37^\circ = 0.8$, and $\sin 37^\circ = 0.6$, what is the height of the observation platform above the ground?

   • A) 32 m
   • B) 48 m
   • C) 80 m
   • D) 16 m
9. 9.

   An environmental monitoring capsule is launched from ground level across flat, horizontal terrain. Telemetry data shows that exactly 2.0 s after launch, the capsule's position vector relative to the launch point is inclined at an angle of 45° above the horizontal. The capsule completes its trajectory and returns to ground level 8.0 s after launch. Assuming air resistance is negligible and taking g = 10 m/s², what was the initial launch speed of the capsule?

   • A) 30 m/s
   • B) 40 m/s
   • C) 50 m/s
   • D) 70 m/s
10. 10.

    During a field test of two meteorological research projectiles, projectile A is launched at an angle of 30° above the horizontal, and projectile B is launched at an angle of 60° above the horizontal over level ground. Telemetry confirms that both projectiles reach the exact same maximum height above the ground during their trajectories. Assuming air resistance is negligible, what is the ratio of the horizontal range of projectile A to that of projectile B, $\frac{R_A}{R_B}$?

    • A) $\frac{1}{3}$
    • B) $\sqrt{3}$
    • C) 3
    • D) $3\sqrt{3}$
11. 11.

    In a sports training facility, an automated ball machine launches a tennis ball from ground level toward a tall vertical screen located at a horizontal distance of $48\text{ m}$. The ball is projected with an initial speed of $30\text{ m/s}$ at an angle of $37^\circ$ above the horizontal. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, $\cos 37^\circ = 0.8$, and $\sin 37^\circ = 0.6$, at what height above the ground does the ball strike the screen?

    • A) 28 m
    • B) 20 m
    • C) 16 m
    • D) 12 m
12. 12.

    A research team launches a sensor capsule across flat terrain to study projectile dynamics. Telemetry records show that the capsule reaches the exact same elevation above the ground at 1 s and 3 s after launch, and it travels a horizontal distance of 30 m between these two instants. Neglecting air resistance and taking g = 10 m/s², what was the launch speed of the capsule?

    • A) 25 m/s
    • B) 20 m/s
    • C) 35 m/s
    • D) 15 m/s
13. 13.

    A coastal rescue drone flying horizontally at an altitude of 45 m with a constant speed of 20 m/s releases an emergency beacon toward a rescue boat. The boat is moving directly away from the drone along the same straight line of motion across calm water at a constant speed of 5 m/s. Neglecting air resistance and taking g = 10 m/s², what must be the horizontal distance between the drone and the boat at the exact moment of release for the beacon to land directly on the boat?

    • A) 30 m
    • B) 45 m
    • C) 60 m
    • D) 75 m
14. 14.

    A wildlife monitoring probe is launched from ground level across flat terrain with an initial speed of 25 m/s at an elevation angle of 53° above the horizontal. Researchers program the probe to activate a downward-facing imaging sensor during its descent when its velocity vector is inclined at 45° below the horizontal. Neglecting air resistance and taking g = 10 m/s², sin 53° = 0.8, and cos 53° = 0.6, how many seconds after launch should the sensor be activated?

    • A) 2.0 s
    • B) 2.5 s
    • C) 3.0 s
    • D) 3.5 s
15. 15.

    An automated probe launches a test capsule across a flat proving ground, and onboard telemetry records that the capsule attains a maximum height of 45 m and a total horizontal range of 240 m before landing at the launch level. Assuming air resistance is negligible and the acceleration due to gravity is $g = 10\text{ m/s}^2$, what was the launch speed of the capsule?

    • A) 30 m/s
    • B) 40 m/s
    • C) 50 m/s
    • D) 70 m/s
16. 16.

    An automated research projectile is launched from flat ground with an initial speed $v_0$ at an elevation angle of $60^\circ$ above the horizontal. During flight data collection, its kinetic energy at the highest point of its parabolic path is recorded as $E_k$. Assuming air resistance is negligible, what was the initial kinetic energy of the projectile at launch?

    • A) $2 E_k$
    • B) $3 E_k$
    • C) $4 E_k$
    • D) $8 E_k$
17. 17.

    During a physics laboratory investigation, a projectile launcher mounted horizontally on a workbench of height h releases a ball with an initial speed v, resulting in a horizontal range R before it hits the floor. The student then raises the launcher to a higher workbench of height 4h and adjusts the launch mechanism so the ball exits horizontally at a speed of 0.5v. Assuming air resistance is negligible, what is the new horizontal range of the ball in terms of R?

    • A) It decreases to 0.25R.
    • B) It decreases to 0.5R.
    • C) It remains equal to R.
    • D) It increases to 2R.