If sally is standing on a 200m tall cliff and throws a ball at 40m/s at a 30° angle to the horizontal: a. what is the ball's initial velocity in the y direction? b. what is the ball's velocity in the x direction? c. how long will it take for the ball to reach its max height? d. what is the ball's max height?

(a) 20 m/s (j) m/s

(b) 20√3 m/s (i) m/s

(c) 2.04 s

(d) 20.4 m

Explanation:

In order to solve the problem, you have to apply the Projectil Motion equations.

For part (a) and (b) you have to obtain the components of the initial velocity vector. The direction forms a 30° angle to the horizontal and the modulus (speed) was given. Therefore:

Applying trigonometric identities (Because the initial velocity is the hypotenuse of a right triangle with angle 30° to the horizontal)

Vx: 40Cos(30°)=20√3 m/s

Vy:40Sin(30°)= 20 m/s

The initial velocity in the y direction is: 20 m/s (j) m/s

The initial velocity in the x direction is: 20√3 m/s (i) m/s

Where i and j are the unit vectors.

For part (c) you have to apply the following vertical motion equation:

Vy=Voy-gt

where Voy is the initial velocity, g is gravity and t is the time

The ball reaches its max height when Vy=0 therefore:

0=Voy-gt

Solving for t:

t=Voy/g=20/9.8= 2.04 seconds

For part (d) you have to apply the other vertical motion equation which is:

y=yo+Voyt-0.5gt²

Where yo is the initial position.

Replacing t=2.04 s, yo=0 m, Voy=20 m/s and solving for y:

y=0+(20)(2.04)-(0.5)(9.8)(2.04)²

y=20.4 m

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

1 a

2 b

3 b

4 d

5 d

6 d

explanation: