Motion in Two Dimensions-Motion in a Plane

Solve the following problem.

A man throws a ball to maximum horizontal distance of 80 m. Calculate the maximum height reached.

Answer the following question.

Show that the path of a projectile is a parabola.

Answer the following question.

Derive the formula for the range and maximum height achieved by a projectile thrown from the origin with initial velocity `vec"u"` at an angle θ to the horizontal.

Solve the following problem.

A particle is projected with speed v₀ at angle θ to the horizontal on an inclined surface making an angle Φ (Φ < θ) to the horizontal. Find the range of the projectile along the inclined surface.

Solve the following problem.

A train is moving eastward at 10 m/sec. A waiter is walking eastward at 1.2m/sec; and a fly is charging toward the north across the waiter’s tray at 2 m/s. What is the velocity of the fly relative to Earth?

Answer the following question.

Derive equations of motion for a particle moving in a plane and show that the motion can be resolved in two independent motions in mutually perpendicular directions.