Horizontal launch Knowledge-Based Practice

Questions

1. 1.

   Two stones are launched horizontally in opposite directions from the top of a tall cliff at the same instant with initial speeds of 5.0 m/s and 20 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, how many seconds after launch are their velocity vectors mutually perpendicular?

   • A) 1.0 s
   • B) 1.5 s
   • C) 2.0 s
   • D) 2.5 s
2. 2.

   A projectile is launched horizontally from the top of a tall cliff. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the initial launch speed of the projectile if its speed 4.0 s after launch is $\sqrt{5}$ times its initial launch speed?

   • A) 20 m/s
   • B) 40 m/s
   • C) 10 m/s
   • D) 80 m/s
3. 3.

   A projectile is launched horizontally from the top of a tall cliff with an initial speed of 15 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the magnitude of the displacement of the projectile between $t = 1.0\text{ s}$ and $t = 3.0\text{ s}$ after launch?

   • A) 30 m
   • B) 40 m
   • C) 50 m
   • D) 70 m
4. 4.

   A projectile is launched horizontally with an initial speed of 40 m/s from the top of a tall cliff. Neglecting air resistance and taking g = 10 m/s², what is the elapsed time from launch when the magnitude of the projectile's vertical displacement is equal to the magnitude of its horizontal displacement?

   • A) 8.0 s
   • B) 6.0 s
   • C) 4.0 s
   • D) 2.0 s
5. 5.

   Two objects, X and Y, are launched horizontally from heights of 20 m and 80 m with initial speeds of 30 m/s and 10 m/s, respectively. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the ratio of the horizontal range of object X to that of object Y ($R_X / R_Y$)?

   • A) 0.75
   • B) 1.50
   • C) 2.00
   • D) 3.00
6. 6.

   A projectile is launched horizontally from a height of 45 m with an initial speed of 20 m/s. Neglecting air resistance and taking g = 10 m/s², what is the magnitude of the average velocity of the projectile from the instant of launch until it strikes the ground?

   • A) 15 m/s
   • B) 20 m/s
   • C) 25 m/s
   • D) 30 m/s
7. 7.

   Two small spheres, A and B, are launched horizontally in the same direction from the same point at the edge of a high cliff at the same instant with initial speeds of 10 m/s and 30 m/s, respectively. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the straight-line distance between the two spheres 2.0 s after launch?

   • A) 20 m
   • B) 60 m
   • C) 80 m
   • D) 40 m
8. 8.

   A stone is launched horizontally from the edge of a cliff. After 4.0 s of flight, the straight line connecting the launch point to the stone's position makes an angle of 53° below the horizontal. Neglecting air resistance, what is the initial horizontal launch speed of the stone? (Take $g = 10\text{ m/s}^2$, $\sin 53^\circ = 0.8$, and $\cos 53^\circ = 0.6$.)

   • A) 10 m/s
   • B) 20 m/s
   • C) 15 m/s
   • D) 30 m/s
9. 9.

   A projectile is launched horizontally at a speed of 20 m/s toward a vertical wall located 60 m away. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the vertical distance the projectile falls before striking the wall?

   • A) 45 m
   • B) 30 m
   • C) 90 m
   • D) 15 m
10. 10.

    A ball is launched horizontally from the edge of a roof. After falling through a vertical distance of 20 m, the magnitude of its total displacement from the launch point is 25 m. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the initial horizontal launch speed of the ball?

    • A) 7.5 m/s
    • B) 10 m/s
    • C) 12.5 m/s
    • D) 15 m/s
11. 11.

    A projectile is launched horizontally from the top of a cliff and strikes the level ground below at an angle of 45° to the horizontal. If the horizontal range of the projectile is 60 m, what is the height of the cliff? (Neglect air resistance and take $g = 10\text{ m/s}^2$.)

    • A) 30 m
    • B) 60 m
    • C) 45 m
    • D) 120 m
12. 12.

    A projectile is launched horizontally from a high platform with an initial speed of 30 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the projectile's speed 4.0 s after launch?

    • A) 30 m/s
    • B) 40 m/s
    • C) 50 m/s
    • D) 70 m/s
13. 13.

    A small object is launched horizontally from the top of a cliff with a speed of 15 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the tangent of the angle that its velocity vector makes with the horizontal after it has fallen a vertical distance of 45 m?

    • A) 2.0
    • B) 1.0
    • C) 0.5
    • D) 3.0
14. 14.

    A metal sphere is launched horizontally from an elevated platform with a speed of 15 m/s and strikes the level ground below with a speed of 25 m/s. Neglecting air resistance and taking the acceleration due to gravity as 10 m/s², what is the height of the platform?

    • A) 10 m
    • B) 20 m
    • C) 30 m
    • D) 40 m
15. 15.

    A small projectile is launched horizontally from the top of an 80 m high cliff with an initial velocity of 25 m/s. Neglecting air resistance and taking $g = 10\text{ m/s}^2$, what is the horizontal distance traveled by the projectile before it strikes the ground?

    • A) 50 m
    • B) 75 m
    • C) 80 m
    • D) 100 m

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