Augustine continues to run around. He gets to the park and has the overwhelming urge to jump off a cliff and try to fly. He does so at an angle of 50 degrees to the horizontal while running at 14.5m/s. With his arms flapping, he rises in the air.

a) what is the highest point from the top of the cliff that he reaches before the laws of physics catch up with him and start bringing him back down to Earth?
b)What is his velocity at that point?
c)If the cliff is 10m high, how long is he in the air before he comes crashing down to the nice, soft, sandy beach below the cliff?
d)what is his final velocity?
e)what is his final horizontal displacement from the cliff?

To answer these questions, we can use the principles of projectile motion. Projectile motion is the motion of an object that is subject only to the force of gravity and air resistance (if applicable). In this case, Augustine's motion can be analyzed as a projectile.

a) To find the highest point Augustine reaches, we need to determine the vertical component of his initial velocity. Augustine's initial velocity can be broken down into horizontal and vertical components using trigonometry. The vertical component can be found by multiplying the initial velocity (14.5 m/s) by the sine of the launch angle (50 degrees).

Vertical component of initial velocity = 14.5 m/s * sin(50°)

b) To find the velocity at the highest point, we know that at this point, the vertical component of velocity will be equal to zero. The horizontal component of velocity remains constant throughout the path, but the vertical component changes due to gravity. Therefore, the velocity at the highest point will have the same horizontal component as the initial velocity but in the opposite direction.

Velocity at highest point = 14.5 m/s * cos(50°)

c) To find the time Augustine spends in the air, we need to determine the time it takes for him to reach the highest point and then double that time since the total time in the air is symmetrical about the highest point. The time to reach the highest point can be found by dividing the vertical component of initial velocity by the acceleration due to gravity (9.8 m/s^2).

Time to reach highest point = (Vertical component of initial velocity) / (acceleration due to gravity)

Total time in the air = 2 * (Time to reach highest point)

d) To find Augustine's final velocity, we need to determine the vertical and horizontal components of velocity when he hits the ground. The vertical component of velocity can be found by multiplying the time in the air by the acceleration due to gravity. The horizontal component of velocity remains constant throughout the path.

Vertical component of final velocity = (acceleration due to gravity) * (Total time in the air)

Final velocity = √((Vertical component of final velocity)^2 + (horizontal component of velocity)^2)

e) To find Augustine's final horizontal displacement from the cliff, we need to determine the horizontal distance he covers in the air. This can be found by multiplying the horizontal component of velocity by the total time in the air.

Horizontal displacement = (horizontal component of velocity) * (Total time in the air)

By plugging in all the known values into these equations, we can find the answers to all the questions.