Question

Basketball player 1 throws the ball 14 m south to player 2, who throws it 24 m east to player 3. Use the Pythagorean theorem to find the displacement (hypotenuse)

Answer 1

The displacement is 27.78 meters at 30.3° south of east

Step-by-step explanation:

Displacement is a vector quantity measuring from the starting position

to the final position

Basketball player 1 throws the ball 14 m south to player 2

Player 2 throws it 24 m east to player 3

The south and east are perpendicular

The displacement is the distance from the position of player 1 to the

position of player 3

The position of player 1 is the origin

The position of player 2 is 14 m south

The position of player 3 is 24 m east

We can find the distance between player 1 and player 3 by using

Pythagorean theorem

→
`h=\sqrt{x^(2)+y^(2)}`

h represents the distance between the 1st and 3rd players

x represents the east distance

y represents the south distance

→ x = 24 , y = 14

→
`h=\sqrt{(24)^(2)+(14)^(2)}=√(576+196)=√(772)=27.78` m

The magnitude of the displacement is 27.78 meters

The direction of the displacement is Ф the angle between the east

and the hypotenuse, then tan Ф = south distance ÷ east distance

→ Ф =
`tan^(-1)(y)/(x)`

→ Ф =
`tan^(-1)(14)/(24)=30.3`°

The direction of the displacement is 30.3° south of east

The displacement is 27.78 meters at 30.3° south of east