A ball is tossed from an upper-story window of a building....

A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of $8.00 \mathrm{~m} / \mathrm{s}$ at an angle of $20.0^{\circ}$ below the horizontal. It strikes the ground $3.00 \mathrm{~s}$ later. (a) How far horizontally from the base of the building does the ball strike the ground? (b) Find the height from which the ball was thrown. (c) How long does it take the ball to reach a point $10.0 \mathrm{~m}$ below the level of launching?

A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of $8.00 \mathrm{~m} / \mathrm{s}$ at an angle of $20.0^{\circ}$ below the horizontal. It strikes the ground $3.00 \mathrm{~s}$ later. (a) How far horizontally from the base of the building does the ball strike the ground?
(b) Find the height from which the ball was thrown.
(c) How long does it take the ball to reach a point $10.0 \mathrm{~m}$ below the level of launching?

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity alone, following a curved trajectory. It is characterized by the independence of its horizontal and vertical motions, where the horizontal motion has constant velocity and the vertical motion has constant acceleration due to gravity.

Vector Decomposition

Vector decomposition is the process of breaking down a velocity vector into its horizontal and vertical components using trigonometric functions. This is essential in projectile motion problems to analyze the separate motions in the horizontal (constant velocity) and vertical (uniform acceleration) directions.

Kinematic Equations

Kinematic equations describe the relationships between displacement, velocity, acceleration, and time for objects moving with constant acceleration. In projectile motion, these equations are used to calculate parameters like displacement and time-of-flight for the vertical motion, and to determine horizontal displacement using constant velocity.

Independence of Motion

The independence of motion is a key principle in projectile problems which states that horizontal and vertical motions occur independently. This allows the motions to be analyzed separately: the horizontal motion is treated as constant velocity motion while the vertical motion is treated as uniformly accelerated motion under gravity.

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