How to Calculate Projectile Distance at an Angle

TL;DR

To calculate the distance a projectile travels when launched at a 30-degree angle with a velocity of 10 meters per second, first determine the vertical component of the velocity to find the time in the air, which is 1.02 seconds. Multiply the horizontal component of the velocity by this time to find that the projectile travels approximately 8.83 meters.

Transcript

• [Voiceover] So I've got a rocket here. And this rocket is going to launch a projectile, maybe it's a rock of some kind, with the velocity of ten meters per second. And the direction of that velocity is going to be be 30 degrees, 30 degrees upwards from the horizontal. Or the angle between the direction of the launch and horizontal is 30 degrees. ... Read More

Key Insights

• 🍳 Trigonometry is used to break down the velocity vector into its vertical and horizontal components.
• 👱 Assuming negligible air resistance simplifies the problem.
• ⌛ The time in the air is calculated by equating the change in velocity in the vertical direction to the acceleration due to gravity multiplied by the time.

Questions & Answers

Q: How is the velocity vector of the projectile broken down into its vertical and horizontal components?

The velocity vector is broken down using trigonometry. The vertical component is determined by multiplying the magnitude of the velocity by the sin of the launch angle.

Q: Why is the assumption made that air resistance is negligible?

Assuming negligible air resistance simplifies the problem and allows for the assumption that the horizontal velocity component remains constant throughout the projectile's flight.

Q: How is the time in the air calculated?

The change in velocity in the vertical direction (from initial to final velocity) is set equal to the acceleration due to gravity multiplied by the time in the air. Solving for the time gives a value of 1.02 seconds.

Q: How is the horizontal displacement calculated?

The horizontal displacement is calculated by multiplying the horizontal velocity component by the time in the air. In this case, the horizontal velocity component is 5 times the square root of 3 meters per second, resulting in an answer of 8.83 meters.

Summary & Key Takeaways

• The video breaks down the velocity vector of the projectile into its vertical and horizontal components to simplify the problem.

• By calculating the vertical component using trigonometry (sin of 30 degrees), it is determined that the projectile stays in the air for 1.02 seconds.

• Assuming the horizontal velocity component remains constant, the total displacement in the horizontal direction is calculated using the horizontal velocity component and the time in the air, resulting in a value of 8.83 meters.