Solved Examples of Horizontal Projectile Motion Problems

📚 Quick Study Guide

• 🚀 Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration due to gravity.
• ➡️ Horizontal motion has constant velocity (neglecting air resistance). The equation is: $x = v_{0x}t$, where $x$ is horizontal distance, $v_{0x}$ is the initial horizontal velocity, and $t$ is time.
• ⬇️ Vertical motion has constant acceleration due to gravity ($g = 9.8 m/s^2$). The relevant equations are: $y = v_{0y}t + \frac{1}{2}gt^2$, $v_y = v_{0y} + gt$, and $v_y^2 = v_{0y}^2 + 2gy$, where $y$ is vertical distance, $v_{0y}$ is initial vertical velocity, and $v_y$ is final vertical velocity.
• ⏱️ Time is the same for both horizontal and vertical motion. Solve for time using the vertical motion equations if needed, then use that time in the horizontal motion equation.
• 🎯 Remember to choose a convenient coordinate system (usually, initial position is (0,0)).

🧪 Practice Quiz

1. A ball is thrown horizontally from the top of a 20-meter-high building with a speed of 5 m/s. How far from the base of the building will the ball hit the ground?
   1. 10.2 m
   2. 20.4 m
   3. 5.1 m
   4. 14.3 m
2. An object is launched horizontally from a height of 45 m with an initial velocity of 20 m/s. What is the time it takes for the object to hit the ground?
   1. 2.0 s
   2. 3.0 s
   3. 4.5 s
   4. 9.0 s
3. A stone is thrown horizontally from a cliff with a velocity of 15 m/s. It hits the ground 3 seconds later. What is the height of the cliff?
   1. 15 m
   2. 30 m
   3. 44.1 m
   4. 90 m
4. A package is dropped from a plane flying horizontally at a constant speed of 80 m/s at an altitude of 500 m. How far horizontally will the package travel before hitting the ground?
   1. 800 m
   2. 500 m
   3. 80 m
   4. 320 m
5. A soccer ball is kicked horizontally off a 1.5 m high platform with an initial velocity of 7 m/s. What is the vertical component of the ball's velocity just before it hits the ground?
   1. -5.42 m/s
   2. -2.94 m/s
   3. -14.7 m/s
   4. 0 m/s
6. A projectile is fired horizontally with an initial velocity of 30 m/s from a height of 100 m. What is the magnitude of the projectile's velocity just before it hits the ground?
   1. 30 m/s
   2. 44.3 m/s
   3. 52.1 m/s
   4. 14 m/s
7. A marble rolls off a table that is 0.8 m high with a horizontal velocity of 2 m/s. What is the horizontal distance the marble travels before hitting the floor?
   1. 0.81 m
   2. 0.91 m
   3. 1.0 m
   4. 1.1 m