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## High school physics

### Course: High school physics>Unit 3

Lesson 5: Projectiles launched at an angle

# Projectiles launched at an angle review

Learn about projectile motion vectors and how the launch angle impacts the trajectory.

## Key terms

TermMeaning
Launch angleThe angle of a projectile’s initial velocity when measured from the horizontal direction. These angles are typically $90\mathrm{°}$ or less.

## Vectors of projectiles launched at an angle

### Constant vertical acceleration

The only acceleration of a projectile is the downwards acceleration due to gravity (see Figure 1 below). Vertical acceleration is always equal to $9.8\phantom{\rule{0.167em}{0ex}}\frac{\text{m}}{{\text{s}}^{2}}$ downward at all points of the trajectory, no matter how a projectile is launched.

### No horizontal acceleration

Nothing accelerates a projectile horizontally, so horizontal acceleration is always zero.

### Horizontal velocity is constant

The projectile’s horizontal speed is constant throughout the entire trajectory (see figure 2 below) because gravity only acts downwards in the vertical direction.

### Vertical velocity changes direction and magnitude during trajectory

Before the object reaches the maximum height, the vertical speed ${v}_{y}$ of a projectile decreases, because acceleration is in the opposite direction. The direction of the velocity is initially upward, since the object’s height is increasing (see Figure 3 below).
Vertical velocity becomes zero at the projectile’s maximum height. The vertical speed increases after the maximum height because acceleration is in the same direction (see figure 3 below). The direction of vertical velocity is downward as the object’s height decreases

## Analyzing angled launch trajectories

### Components of initial velocity

To see how to break down the total velocity vector into the horizontal and vertical components using trigonometry, see the article on analyzing vectors.

### Launch angle trajectory comparisons

The diagram below shows trajectories for different launch angles that have the same initial speed. The launch angle determines the maximum height, time in the air, and maximum horizontal distance of the projectile.

### Higher launch angles have higher maximum height

The maximum height is determined by the initial vertical velocity. Since steeper launch angles have a larger vertical velocity component, increasing the launch angle increases the maximum height. (see figure 5 above).

### Higher launch angles have greater times in the air

The time in air is determined by the initial vertical velocity. Since steeper launch angles have a larger vertical velocity component, increasing the launch angle increases the time in air. For deeper explanations of the relationship between projectile time in air and initial vertical velocity, see Sal’s video on the optimal angle for a projectile.

### Projectile maximum horizontal distance depends on horizontal velocity and time in air

Launch angles closer to $45\mathrm{°}$ give longer maximum horizontal distance (range) if initial speed is the same (see figure 5 above). These launches have a better balance of the initial velocity components that optimize the horizontal velocity and time in air (see figure 4).

## Common misconceptions

• People mix up horizontal vs. vertical components of acceleration and velocity. The acceleration is a constant downwards $9.8\phantom{\rule{0.167em}{0ex}}\frac{\text{m}}{{s}^{2}}$ (see figure 1) because gravity is the only source of acceleration. This acceleration only changes the vertical velocity, so the horizontal velocity is constant.
• People can’t remember what is zero at the maximum height. Vertical velocity is zero at this point, but there is still horizontal velocity and acceleration is still down.