An athlete performing a long jump leaves the ground at a 27.0 degree angle and lands 7.80m away. what was the takeoff speed?

The initial velocity is 9.72 m/s.

Since an athlete performs a projectile motion;

R = u^2sin2θ/g

R = u^2sin2θ/g

Rg = u^2sin2θ

u^2 =Rg/sin2θ

u = √Rg/sin2θ

u = √7.80 × 9.8/sin(2)27.0

u = 9.72 m/s

The initial velocity is 9.72 m/s.

Learn more about projectiles: link

=9.72 m/s

Explanation:

From the Newton's laws of motion;

x=2(v²cos∅sin∅)/g

Using geometry we see that 2 cos∅sin∅ = sin 2∅

Therefore, x= (v²sin 2∅)g,  where v is the take off speed x the range and ∅ the launch angle.

Making v the subject of the formula we obtain the following equation.

v=√{xg /(sin 2∅)}

x=7.80

∅=27.0

v=√{7.8×9.8/sin(27×2)}

v=√94.485

v=9.72 m/s

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.