Question

Justin Bieber is thrown horizontally at 10.0 m/s from the top of a cliff 122.5 m high.

How long does it take to reach the ground?
What is the horizontal displacement?
What is Justin's final velocity?

Answer 1

===> Distance fallen from rest in free fall =

(1/2) (acceleration) (time²)

(122.5 m) = (1/2) (9.8 m/s²) (time²)

Divide each side by (4.9 m/s²): (122.5 m / 4.9 m/s²) = time²

(122.5/4.9) s² = time²

Take the square root of each side: 5.0 seconds

===> (Accelerating at 9.8 m/s², he will be dropping at

(9.8 m/s²) x (5.0 s) = 49 m/s

when he goes 'splat'. We'll need this number for the last part.)

===> With no air resistance, the horizontal component of velocity

doesn't change.

Horizontal distance = (10 m/s) x (5.0 s) = 50 meters .

===> Impact velocity = (10 m/s horizontally) + (49 m/s vertically)

= √(10² + 49²) = 50.01 m/s arctan(10/49)

= 50.01 m/s at 11.5° from straight down,

away from the base of the cliff.

Step-by-step explanation:

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Answer 2

===> Distance fallen from rest in free fall =

(1/2) (acceleration) (time²)

(122.5 m) = (1/2) (9.8 m/s²) (time²)

Divide each side by (4.9 m/s²): (122.5 m / 4.9 m/s²) = time²

(122.5/4.9) s² = time²

Take the square root of each side: 5.0 seconds


===> (Accelerating at 9.8 m/s², he will be dropping at
(9.8 m/s²) x (5.0 s) = 49 m/s
when he goes 'splat'. We'll need this number for the last part.)


===> With no air resistance, the horizontal component of velocity
doesn't change.

Horizontal distance = (10 m/s) x (5.0 s) = 50 meters .

===> Impact velocity = (10 m/s horizontally) + (49 m/s vertically)

= √(10² + 49²) = 50.01 m/s arctan(10/49)

= 50.01 m/s at 11.5° from straight down,
away from the base of the cliff.