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Classical Mechanics

2D Kinematics

2D Kinematics - Problem Solving


An airplane is taking off on the runway. At the moment the wheels leave the ground, the plane is traveling at \( 60 \text{ m/s} \) horizontally. The wings generate a lift which causes a vertical acceleration of \( 1 \text{ m/s}^2 ,\) and the jets produce a horizontal acceleration of \( 2 \text{ m/s}^2 .\) When the airplane is flying at an altitude of \( 3200 \text{ m}, \) what is its horizontal distance from the airport?

The air resistance is negligible.

A hunter aims directly at a target \( 66 \text{ m} \) away, at the same height as the gun. If the bullet is fired at a speed of \( 66 \text{ m/s}, \) by how much will the bullet miss the target?

NOTES: The air resistance is negligible, and the gravitational acceleration is \(g=10\text{ m/s}^2.\) You may also assume the bullet does not hit the ground until after passing the target.

A boy throws a ball at \( 32 \sqrt{2} \text{ m/s} \) at a \( 45^ \circ \) angle with the ground. Find the horizontal distance the ball flies.

Gravitational acceleration is \( g =10 \text{ m/s}^2, \) and air resistance is negligible.

A ball is thrown horizontally at \( 16 \text{ m/s} .\) If the ball travels a horizontal distance of \( 80 \text{ m} \) before hitting the ground, from what height was the ball thrown?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

A car initially at rest accelerates uniformly at a rate of \( (6 \text{ m/s}^2) \hat{i}.\) If the car travels \( (108 \text{ m}) \hat{i} ,\) what is its final velocity?


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