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# ZingPath: Acceleration Due to Gravity

## Projectiles Launched Vertically               Searching for

## Acceleration Due to Gravity

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### Lesson Focus

#### Projectiles Launched Vertically

Physics

You will examine how mass and initial velocity affect the motion of a vertically launched object.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Explain that as the initial velocity increases, the duration of the flight of a projectile launched vertically upward also increases.
• Explain that as the initial velocity increases, the maximum height of a projectile launched vertically upward also increases.
• Explain that when the initial velocity is kept the same, changing the mass of a vertically launched projectile does not affect the time of flight.
• Explain that when the initial velocity is kept constant, changing the mass of a vertically launched projectile does not affect its maximum height.

### Everything You'll Have Covered

Projectiles launched vertically move under a constant acceleration due to the force of gravity between the object and Earth.

As projectiles move upward, their speed decreases by 9.8 m/s each second. (It is generally acceptable to round this change in velocity to 10 m/s each second.) Due to this decrease in speed, the projectile moves a smaller distance each second, until it reaches its maximum height. At the top of the curve, the object's velocity is 0 m/s. However, since its velocity is changing by about 10 m/s every second, its acceleration is still about 10 m/s/s at all points during its flight. Due to this constant acceleration, the initial velocity is directly proportional to the time of flight. For example, a projectile launched vertically at a velocity of 40 m/s will take approximately four seconds to reach the top of the curve and another four seconds to get back to its initial height. One second after it's launched, it will be moving 30 m/s. One second later, it will be moving 20 m/s; one second later, it will be moving 10 m/s. One more second later, it will reach its maximum height, where its velocity will be 0 m/s. The projectile changes direction and moves back toward Earth with its speed increasing by 10 m/s each second, in perfect symmetry with its path upward.

When air resistance is negligible, the mass of the object does not affect the maximum height or the time spent in the air. However, the initial velocity of the projectile does play a role. As you increase the initial velocity of the projectile, the time of flight and maximum height also increase.

### Tutorial Details

 Approximate Time 20 Minutes Pre-requisite Concepts Students should be familiar with constant velocity, constant acceleration, and gravity. Course Physics Type of Tutorial Concept Development Key Vocabulary acceleration, freefall, gravity