Projectile Motion, Launched from a Known Height

TL;DR

Calculate the distance a ball lands from a cliff when kicked with an initial horizontal velocity of 17.5 m/s.

Transcript

okay this problem I've entitled falling projectile motion and the question is this if a ball is kicked off a cliff that's 14 M high and has an initial horizontal velocity of 17.5 m/s how far from the cliff does the ball land so what we really want to solve for in this case is we want to know this distance in the X Direction oops all right and we ca... Read More

Key Insights

• 😒 Horizontal motion remains unaffected by gravity, allowing for the use of simpler equations.
• 😀 The parabolic path of a falling projectile is a result of the increasing velocity in the y-direction due to gravity.
• ❣️ Keeping velocities and accelerations in the x and y-directions separate is crucial for accurate calculations.
• 💬 Using known values and equations, the time it takes for a ball to fall and the distance it lands from a cliff can be determined.
• 😀 The time for an object to fall is determined only by the height and acceleration in the y-direction.
• ✖️ The distance in the x-direction can be calculated by multiplying the initial velocity in the x-direction by the time.

Questions & Answers

Q: How does the initial velocity in the x-direction affect the ball's motion?

The initial velocity in the x-direction remains constant throughout the ball's flight, resulting in a horizontal path unaffected by gravity.

Q: What is the relationship between velocity in the y-direction and time?

The velocity in the y-direction starts at 0 m/s and increases as gravity accelerates the ball downward. The relationship between velocity and time is quadratic.

Q: Why is it necessary to keep the velocities and accelerations in the x and y-directions separate?

Velocities and accelerations in the x and y-directions are independent of each other due to gravity acting only in the y-direction. Combining them in a single equation would result in incorrect calculations.

Q: How is the time it takes for the ball to fall calculated?

Using the equation dy = (1/2) * ay * t^2, where dy is the height of the cliff (14m) and ay is the acceleration in the y-direction (-9.8 m/s^2), the time is found to be 1.69 seconds.

Summary & Key Takeaways

• A ball kicked horizontally off a 14m high cliff follows a parabolic path due to the force of gravity acting only in the y-direction.

• The initial velocity in the x-direction remains constant at 17.5 m/s, while the velocity in the y-direction increases due to acceleration from gravity.

• By using equations and known values, the time it takes for the ball to fall (1.69 seconds) and the distance it lands from the cliff (29.58m) can be calculated.