Directions: This section of the exam consists of questions...

Directions: This section of the exam consists of questions or incomplete statements followed by five possible answers or completions. Select the best answer or completion, and fill in the corresponding bubble on the answer sheet. A ball is thrown horizontally with a speed $v$ drops a distance $y$ and moves horizontally a distance $x .$ If the ball is thrown with the same horizontal speed $v$ from a height of $2 y,$ what is its new horizontal displacement? (A) $X$ (B) $\sqrt{2} X$ (C) 2$x$ (D) 4$x$ (E) 16$x$

Directions: This section of the exam consists of questions or incomplete statements followed by five possible answers or completions. Select the best answer or completion, and fill in the corresponding bubble on the answer sheet.

A ball is thrown horizontally with a speed $v$ drops a distance $y$ and moves horizontally a distance $x .$ If the ball is thrown with the same horizontal speed $v$ from a height of $2 y,$ what is its new horizontal displacement?
(A) $X$
(B) $\sqrt{2} X$
(C) 2$x$
(D) 4$x$
(E) 16$x$

Key Concepts

Projectile Motion

Projectile motion describes the motion of an object thrown into the air, where gravity only affects the vertical component of the motion while the horizontal component remains constant (assuming no air resistance). This separation of motion is fundamental in analyzing trajectories in physics.

Time of Flight

Time of flight is the duration an object stays in the air before reaching the ground, which, in the absence of an initial vertical velocity, depends solely on the height from which it is released and the acceleration due to gravity. The time increases with the square root of the drop height, meaning that if the height is doubled, the time of fall is multiplied by the square root of 2.

Horizontal Displacement

Horizontal displacement in projectile motion is determined by multiplying the constant horizontal speed by the time of flight. Since the horizontal speed does not change, any factor that increases the time of flight, such as an increase in drop height, will directly increase the horizontal displacement.

Transcript

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