Angled launch Transitional Reasoning Download PDF

Questions

1. 1.

   During a field test on flat horizontal ground, an automated launcher fires a projectile into the air. An optical tracking system records that the projectile reaches its highest point at a horizontal distance of 60 m and an elevation of 45 m relative to the launch position. Neglecting air resistance and taking the acceleration due to gravity as 10 m/s², what is the magnitude of the projectile's average velocity from launch until it reaches its highest point?

   • A) 25 m/s
   • B) 35 m/s
   • C) 20 m/s
   • D) 15 m/s
2. 2.

   During a field test on flat horizontal ground, a projectile is launched from ground level at an angle above the horizontal. Trajectory tracking data reveal that the projectile reaches its maximum height at $t = 2.0\text{ s}$, and the straight-line displacement between its positions at $t = 1.0\text{ s}$ and $t = 3.0\text{ s}$ has a magnitude of 30 m. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what was the initial launch speed of the projectile?

   • A) 15 m/s
   • B) 20 m/s
   • C) 35 m/s
   • D) 25 m/s
3. 3.

   During a field trial on flat ground, a research projectile is launched from ground level at an angle of 45° above the horizontal. Trajectory tracking confirms that the projectile attains a maximum height of 80 m above the ground. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the straight-line distance from the launch point to the projectile at 2.0 s after launch?

   • A) 80 m
   • B) 100 m
   • C) 120 m
   • D) 140 m
4. 4.

   During a robotics competition held on flat ground, a launcher shoots a projectile toward a target located at ground level at a horizontal distance of 60 m. A sensor confirms that at a horizontal distance of 15 m from the launch position, the projectile reaches an elevation of 9 m above the ground before landing directly on the target. Neglecting air resistance and taking the acceleration due to gravity as 10 m/s², what is the maximum height attained by the projectile during its trajectory?

   • A) 12 m
   • B) 15 m
   • C) 16 m
   • D) 18 m
5. 5.

   During a field trial on flat horizontal ground, a projectile is launched from ground level. A tracking system determines that the projectile has a total flight time of 6.0 s and lands at a horizontal range of 90 m. Neglecting air resistance and taking the acceleration due to gravity as 10 m/s², what is the speed of the projectile when it passes through an altitude of 25 m above the ground?

   • A) 25 m/s
   • B) 20 m/s
   • C) 30 m/s
   • D) 35 m/s
6. 6.

   During a field demonstration on flat horizontal ground, two projectiles, X and Y, are launched simultaneously from ground level. Both projectiles attain the same maximum height of 45 m. Projectile X has a horizontal velocity component of 15 m/s, while Projectile Y lands 150 m farther downrange than Projectile X. Neglecting air resistance and taking g = 10 m/s², what is the launch speed of Projectile Y?

   • A) 35 m/s
   • B) 40 m/s
   • C) 50 m/s
   • D) 70 m/s
7. 7.

   During a field trial on flat ground, a research projectile is launched from ground level at an angle of $53^\circ$ above the horizontal. A tracking sensor records that the projectile passes through a target point located at a horizontal distance of $36\text{ m}$ from the launch position and at a vertical height of $28\text{ m}$ above the ground. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, what was the initial launch speed of the projectile?

   • A) $18\text{ m/s}$
   • B) $24\text{ m/s}$
   • C) $40\text{ m/s}$
   • D) $30\text{ m/s}$
8. 8.

   During a field test on level ground, a projectile is launched at an angle above the horizontal and lands at the same elevation after a total flight time of 6.0 s. At the instant the projectile reaches its maximum height, a stationary optical tracking sensor located at the launch point detects it at an angle of elevation $\phi$, where $\tan\phi = 0.75$. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the total horizontal range of the projectile?

   • A) 60 m
   • B) 120 m
   • C) 180 m
   • D) 240 m
9. 9.

   During a field test on a flat horizontal proving ground, an automated launcher fires a projectile into the air. Trajectory sensors record that the projectile attains a maximum height of 125 m above the ground. Later, during its descent at an altitude of 80 m, the projectile's velocity vector makes an angle of 45° below the horizontal. Neglecting air resistance and taking g = 10 m/s², what is the total horizontal range of the projectile?

   • A) 150 m
   • B) 200 m
   • C) 300 m
   • D) 400 m
10. 10.

    In an experimental trial over flat ground, two identical projectiles are launched with the same initial speed at complementary angles, landing at the exact same horizontal position. The projectile launched at the steeper angle has a total flight time of 4.0 s, whereas the one launched at the shallower angle has a flight time of 3.0 s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the common horizontal range achieved by these projectiles?

    • A) 60 m
    • B) 80 m
    • C) 120 m
    • D) 140 m
11. 11.

    A rescue team positioned on the edge of an 80 m high vertical cliff launches a supply capsule with an initial speed of 50 m/s at an angle of 37° above the horizontal toward a marked zone at sea level. Assuming the sea surface is flat and neglecting air resistance, what is the horizontal distance from the base of the cliff to the point where the capsule lands in the water? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.6$, and $\cos 37^\circ = 0.8$.)

    • A) 160 m
    • B) 200 m
    • C) 240 m
    • D) 320 m
12. 12.

    An emergency supply capsule is launched from ground level with an initial speed of 25 m/s at an angle of 53° above the horizontal toward the flat roof of a building 15 m above the ground. The capsule reaches its peak altitude and then lands on the roof during its descent. Neglecting air resistance, what is the horizontal distance from the launch point to the landing position on the roof? (Take g = 10 m/s², sin 53° = 0.8, and cos 53° = 0.6.)

    • A) 15 m
    • B) 30 m
    • C) 45 m
    • D) 60 m
13. 13.

    A high-speed camera records the trajectory of a projectile launched from flat ground at an angle above the horizontal. Software analysis indicates that the projectile remains at or above an elevation of 15 m for a continuous duration of 2.0 s before descending back toward the surface. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the maximum height reached by the projectile during its flight?

    • A) 17.5 m
    • B) 25.0 m
    • C) 30.0 m
    • D) 20.0 m
14. 14.

    During an experimental trial on flat ground, a motion-sensor system tracks a small projectile launched from ground level. The sensor records that exactly 1 s after launch, the projectile's velocity vector makes an angle of 45° above the horizontal, and at 2 s after launch, it reaches its maximum height. Neglecting air resistance and taking g = 10 m/s², what is the total horizontal range of the projectile?

    • A) 20 m
    • B) 30 m
    • C) 40 m
    • D) 60 m
15. 15.

    An agricultural device launches a biodegradable seed capsule from ground level over a flat field. The capsule is designed to burst and release its contents at the highest point of its trajectory, which an onboard sensor registers exactly 2 s after launch. If the straight-line distance from the launch point to the burst point is measured to be 25 m, what is the horizontal distance traveled by the capsule from launch until it bursts? (Neglect air resistance and take $g = 10\text{ m/s}^2$.)

    • A) 10 m
    • B) 15 m
    • C) 20 m
    • D) 25 m
16. 16.

    During a ballistics trial conducted on flat, horizontal ground, a projectile is launched from ground level at an angle above the horizontal. A tracking system records that the projectile reaches a maximum height of 20 m and that its speed at this highest point is exactly 60% of its initial launch speed. Neglecting air resistance and taking the acceleration due to gravity as 10 m/s², what is the total horizontal range of the projectile?

    • A) 60 m
    • B) 80 m
    • C) 30 m
    • D) 100 m
17. 17.

    A rescue probe is launched from flat ground with an initial speed of 50 m/s at an angle of 53° above the horizontal. During its descent, an internal mechanism deploys a recovery parachute at the exact instant the velocity vector of the probe is directed at 45° below the horizontal. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, how much time elapses between launch and the deployment of the parachute?

    • A) 1 s
    • B) 4 s
    • C) 7 s
    • D) 8 s
18. 18.

    During a field trial on flat ground, a projectile tracking system records that an object launched at an angle reaches a maximum height of 45 m and lands at a horizontal range of 240 m. Assuming air resistance is negligible and taking the acceleration due to gravity as 10 m/s², what is the initial launch speed of the projectile?

    • A) 40 m/s
    • B) 50 m/s
    • C) 70 m/s
    • D) 80 m/s
19. 19.

    An automated launcher fires a projectile from ground level with an initial kinetic energy of 500 J and an initial speed of 20 m/s. At the highest point of its trajectory, where its motion is purely horizontal, the kinetic energy of the projectile is measured to be 320 J. Neglecting air resistance and taking the acceleration due to gravity as 10 m/s², what is the maximum height reached by the projectile above the ground?

    • A) 4.5 m
    • B) 7.2 m
    • C) 9.0 m
    • D) 12.8 m
20. 20.

    A student evaluates whether a ball launched from ground level at an angle of $37^\circ$ above the horizontal with a speed of $20\text{ m/s}$ can clear a $2.2\text{ m}$ tall defensive barrier placed $16\text{ m}$ horizontally from the launch point. Neglecting air resistance, what is the vertical height of the ball at the moment it reaches the horizontal position of the barrier, and does it clear the barrier? (Take $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.6$, and $\cos 37^\circ = 0.8$.)

    • A) $5.0\text{ m}$, so it clears the barrier
    • B) $2.0\text{ m}$, so it does not clear the barrier
    • C) $12.0\text{ m}$, so it clears the barrier
    • D) $7.0\text{ m}$, so it clears the barrier