Angled launch Transitional Reasoning Practice

Questions

1. 1.

   During a ballistics trial conducted over level horizontal ground, two test projectiles, A and B, are launched from the same location with the same initial speed $v_0$. Projectile A is launched at an angle of 45° above the horizontal and lands at a total horizontal range of 160 m. Projectile B is launched at an angle of 60° above the horizontal. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, and $\sin 60^\circ = \frac{\sqrt{3}}{2}$, what is the maximum height above the ground reached by Projectile B?

   • A) 40 m
   • B) 80 m
   • C) 120 m
   • D) 60 m
2. 2.

   During a ballistics trial conducted over level horizontal ground, a test projectile is launched at an angle above the horizontal. Telemetry records show that the projectile attains a maximum height of 45 m and that its speed at this highest point is 15 m/s. Assuming air resistance is negligible and $g = 10\text{ m/s}^2$, what is the speed of the projectile when it is at a height of 25 m above the ground?

   • A) 25 m/s
   • B) 20 m/s
   • C) 30 m/s
   • D) 35 m/s
3. 3.

   During a ballistics trial on flat horizontal ground, an optical tracking sensor stationed at the launch position tracks a projectile. Telemetry records that when the projectile reaches its maximum height, the line of sight from the launch position to the projectile is inclined at an angle above the horizontal whose tangent is 0.5. If the projectile remains in the air for a total flight time of 6.0 s, what is its total horizontal range upon landing? (Assume air resistance is negligible and g = 10 m/s².)

   • A) 90 m
   • B) 120 m
   • C) 180 m
   • D) 360 m
4. 4.

   During a ballistics trial conducted over level horizontal terrain, telemetry sensors track a projectile from launch to touchdown. The data shows that the kinetic energy of the projectile at its maximum height is exactly 36% of its initial launch kinetic energy, and its total time of flight is 8.0 s. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what is the total horizontal range achieved by the projectile?

   • A) 240 m
   • B) 180 m
   • C) 120 m
   • D) 320 m
5. 5.

   During a dual-projectile tracking trial on flat horizontal terrain, projectiles A and B are launched simultaneously from the same origin with the same initial speed of 50 m/s. Projectile A is launched at an angle of 53° above the horizontal, while projectile B is launched at an angle of 37° above the horizontal. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 53^\circ = \cos 37^\circ = 0.8$, and $\cos 53^\circ = \sin 37^\circ = 0.6$, what is the straight-line distance between the two projectiles at the instant projectile B reaches its maximum height?

   • A) 30 m
   • B) $30\sqrt{2}\text{ m}$
   • C) 45 m
   • D) 60 m
6. 6.

   During an obstacle-clearance trial on level ground, a projectile is launched from ground level and grazes the top of a 15 m tall vertical barrier located at a horizontal distance of 15 m from the launch site. The projectile continues along its parabolic trajectory and lands back on the ground at a total horizontal range of 60 m from the launch site. Assuming air resistance is negligible and $g = 10\text{ m/s}^2$, what is the maximum height above the ground reached by the projectile?

   • A) 16 m
   • B) 18 m
   • C) 20 m
   • D) 25 m
7. 7.

   During a field test, an automated launcher fires a supply container from flat ground toward a landing platform elevated 25 m above the ground. The container is launched with an initial speed of 50 m/s at an angle of 37° above the horizontal and touches down on the platform during the descent phase of its flight. Assuming air resistance is negligible, g = 10 m/s², sin 37° = 0.6, and cos 37° = 0.8, what is the horizontal distance from the launch point to the touchdown point on the platform?

   • A) 40 m
   • B) 120 m
   • C) 160 m
   • D) 200 m
8. 8.

   An automated interceptor system stationed on flat ground tests a tracking mechanism against an aerial target. A test target is held stationary at a height of 80 m above the ground and at a horizontal distance of 60 m from the launcher. The launcher aims directly along the line of sight toward the target and fires a projectile with an initial speed of 50 m/s at the exact instant the target is released from rest to fall freely under gravity. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, at what height above the ground does the projectile strike the falling target?

   • A) 40 m
   • B) 60 m
   • C) 50 m
   • D) 70 m
9. 9.

   A rescue team stationed on top of a vertical coastal cliff 80 m above sea level launches an emergency supply package toward a boat in the water. The launcher fires the package with an initial speed of 50 m/s at an angle of 37° above the horizontal. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.6$, and $\cos 37^\circ = 0.8$, what is the horizontal distance from the base of the cliff to the point where the package strikes the water?

   • A) 240 m
   • B) 320 m
   • C) 200 m
   • D) 360 m
10. 10.

    An automated ballistics system launches a test projectile across level ground with an initial speed of 40 m/s at an angle of 53° above the horizontal. Onboard sensors record flight data until the projectile's instantaneous velocity vector becomes perpendicular to its initial launch velocity vector. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, what is the speed of the projectile at this instant?

    • A) 18 m/s
    • B) 24 m/s
    • C) 30 m/s
    • D) 32 m/s
11. 11.

    During a field trial on level horizontal ground, a projectile is launched such that its total horizontal range is exactly three times its maximum height. Telemetry sensors record that the projectile attains a maximum height of 80 m above the ground. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what is the initial launch speed of the projectile?

    • A) 50 m/s
    • B) 40 m/s
    • C) 70 m/s
    • D) 30 m/s
12. 12.

    During a field test, an automated research probe is launched from flat ground with an initial horizontal velocity component of 30 m/s and an initial vertical velocity component of 80 m/s. Assuming air resistance is negligible and $g = 10\text{ m/s}^2$, what is the magnitude of the average velocity of the probe from the instant of launch until it reaches its maximum height?

    • A) 30 m/s
    • B) 40 m/s
    • C) 50 m/s
    • D) 55 m/s
13. 13.

    An automated launcher fires a test projectile across flat horizontal ground with an initial speed of 50 m/s at an angle of 53° above the horizontal. During the descent phase of the trajectory, an optical tracking sensor detects that the projectile's velocity vector is directed at an angle of 45° below the horizontal. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, what horizontal distance has the projectile traveled from the launch point at this instant?

    • A) 30 m
    • B) 120 m
    • C) 150 m
    • D) 210 m
14. 14.

    An automated research launcher fires a sensor projectile across flat horizontal ground with an initial speed of 50 m/s at an angle of 53° above the horizontal. An onboard scientific instrument is programmed to collect atmospheric data only while the projectile is at or above 75% of its maximum height. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$, what horizontal distance does the projectile cover while the instrument is actively collecting data?

    • A) 60 m
    • B) 120 m
    • C) 180 m
    • D) 240 m
15. 15.

    A research projectile launched from level ground is tracked by telemetry sensors during its ascent. The data shows that 2 s after launch, its velocity vector is inclined at 45° above the horizontal, and at 5 s after launch, it reaches its maximum height. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s², what is the total horizontal range of the projectile when it lands?

    • A) 150 m
    • B) 300 m
    • C) 200 m
    • D) 400 m
16. 16.

    An automated tracking system records the flight of a test projectile launched at an angle above level horizontal ground. The sensor data indicates that at $t = 1\text{ s}$ and $t = 3\text{ s}$ after launch, the projectile is at the exact same vertical height, and during this 2-second interval, it covers a horizontal distance of 30 m. Assuming air resistance is negligible and $g = 10\text{ m/s}^2$, what is the initial launch speed of the projectile?

    • A) 25 m/s
    • B) 35 m/s
    • C) 20 m/s
    • D) 50 m/s
17. 17.

    An agricultural engineer tests a robotic irrigation system that launches water projectiles at a constant initial speed of 50 m/s across level ground to deliver water to a specific target zone. The control system achieves the required horizontal range by using two complementary launch angles, $\theta_1 = 53^\circ$ and $\theta_2 = 37^\circ$. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 53^\circ = \cos 37^\circ = 0.8$, and $\cos 53^\circ = \sin 37^\circ = 0.6$, what is the difference between the maximum heights reached along these two trajectories, $h_1 - h_2$?

    • A) 35 m
    • B) 25 m
    • C) 50 m
    • D) 70 m
18. 18.

    A tracking device on flat ground monitors a projectile launched at an angle above the horizontal. The sensor records that the projectile reaches its highest point 3 s after launch, moving with a speed of 20 m/s at that instant. Assuming air resistance is negligible and the acceleration due to gravity is 10 m/s^2, what are the maximum height attained by the projectile and its total horizontal range upon landing?

    • A) Maximum height is 30 m; horizontal range is 60 m.
    • B) Maximum height is 45 m; horizontal range is 60 m.
    • C) Maximum height is 90 m; horizontal range is 120 m.
    • D) Maximum height is 45 m; horizontal range is 120 m.
19. 19.

    During a field trial on flat horizontal ground, a launcher fires a small projectile at an angle of 30° above the horizontal with an initial speed of 40 m/s toward a tall vertical target. The target is located at a horizontal distance of $60\sqrt{3}\text{ m}$ from the launch position. Assuming air resistance is negligible, $g = 10\text{ m/s}^2$, $\sin 30^\circ = 0.5$, and $\cos 30^\circ = \frac{\sqrt{3}}{2}$, at what height above the ground does the projectile hit the target, and what is its vertical direction of motion at impact?

    • A) 15 m, descending
    • B) 15 m, ascending
    • C) 20 m, descending
    • D) 25 m, ascending
20. 20.

    In a physics laboratory, a small sphere is launched from flat horizontal ground with an initial kinetic energy of $E$ at an angle of 60° above the horizontal. Assuming air resistance is negligible, what are the kinetic energy of the sphere at its maximum height and the work done by gravity on the sphere during the ascent to this point?

    • A) $\frac{1}{4}E$ and $-\frac{3}{4}E$
    • B) $\frac{1}{2}E$ and $-\frac{1}{2}E$
    • C) $\frac{1}{4}E$ and $-E$
    • D) 0 and $-E$

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