Question

x.Hm of the motions described below, determine the algebraic sign (positive, negative, or zero) of the xcomponent and y component of velocity of the object at the time specified. For all of the motions, the positive xaxis points to the right and the positive y axis points upward.

Alex, a mountaineer, must leap across a wide crevasse. (Intro 1 figure) The other side of the crevasse is below the point from which he leaps, as shown in the figure. Alex leaps horizontally and successfully makes the jump.

Part A

Determine the algebraic sign of Alex's x velocity and y velocity at the instant he leaves the ground at the beginning of the jump.

Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,-and 0,+).

Part B

Determine the algebraic signs of Alex's x velocity and y velocity the instant before he lands at the end of the jump.

Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+).

At the buzzer, a basketball player shoots a desperation shot. The ball goes in! (Intro 2 figure)

Part C

Determine the algebraic signs of the ball's x velocity and y velocity the instant after it leaves the player's hands.

Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+).

art D

Determine the algebraic signs of the ball's x velocity and y velocity at the ball's maximum height.

Type the algebraic signs of the x velocity and the y velocity separated by a comma (examples: +,- and 0,+).

Answer 1

Concepts and reason

The direction of velocity at different instants of time is used to determine the algebraic signs of the $x$ velocity which means velocity along the horizontal and $y$ velocity which means velocity along the vertical. The $x$ velocity has $+$ algebraic sign if the object moves rightward, $-$ algebraic sign if the object moves leftward, and $0$ if the object neither moves leftward nor rightwards. The $y$ velocity has $+$ algebraic sign if the object moves upward, $-$ sign if the object moves downward, and $0$ if the object neither moves upward nor downwards.

Fundamentals

The $x$ velocity has $+$ algebraic sign if the object moves rightward, $-$ algebraic sign if the object moves leftward, and $0$ if the object neither moves leftward nor rightwards.

The $y$ velocity has $+$ algebraic sign if the object moves upward, $-$ sign if the object moves downward, and $0$ if the object neither moves upward nor downwards.

Part A

Alex jumps moving rightward in the horizontal direction initially. The other side is down so during the jump in air, the acceleration of gravity will pull him down. At the instant of the jump Alex will leave the ground with velocity only along the horizontal and no upward or downward velocity will be there. For a velocity, rightwards along the horizontal or $x$ axis, the algebraic sign of the $x$ velocity will be $+$. The $y$ velocity is neither upward nor downwards that is $0$ as Alex jumps right from the edge of the mountain.

Part B

Alex jumps moving rightward in the horizontal direction initially. The other side is down so during the jump in air, the acceleration of gravity will pull him down. Alex will reach the other side of the crevasse with velocity which is rightward along the horizontal and downward along the vertical. For a velocity, rightwards along the horizontal or $x$ axis, the algebraic sign of the $x$ velocity will be $+$. For a velocity, downwards along the vertical or $y$ axis, the algebraic sign of the $y$ velocity will be $-$.

Part C

The ball will move upwards and rightwards as it leaves the player’s hands. While travelling in air, the acceleration of gravity will pull it down. The hoop is higher in height and the ball should be given an initial vertical velocity so that it can move upward enough to reach the height of the hoop. For a velocity, rightwards along the horizontal or $x$ axis, the algebraic sign of the $x$ velocity will be $+$. For a velocity, upwards along the vertical or $y$ axis, the algebraic sign of the $y$ velocity will be $+$.

Part D

The ball will move upwards and rightwards as it leaves the player’s hands. While travelling in air, the acceleration of gravity will pull it down. The hoop is higher in height and the ball would be travelling upwards to downwards as it goes through the hoop. The ball will reach the maximum height just before it starts falling again. The velocity of the ball at the maximum height will only be rightward and no upward or downward velocity will be there. For a velocity, rightwards along the horizontal or $x$ axis, the algebraic sign of the $x$ velocity will be $+$. The $y$ velocity is neither upward nor downwards that is $0$.

Ans: Part A

The algebraic sign of Alex’s $x$ velocity and $y$ velocity at the instance he leaves the ground at the beginning of the jump are $+ ,0$.