Problem 7: a baseball slugger hits a pitch and watches the ball fly into the bleachers for a home run, landing h = 9.5 m higher than it was struck. when visiting with the fan that caught the ball, he learned the ball was moving with final velocity vf = 39.6 m/s at an angle θf = 33° below horizontal when caught. assume the ball encountered no air resistance, and use a cartesian coordinate system with the origin located at the ball's initial position.

(a) calculate the ball’s initial vertical velocity, v0y, in m/s.
(b) calculate the magnitude of the ball’s initial velocity, v0, in m/s.
(c) find the angle θ0 in degrees above the horizontal at which the ball left the bat.

Part a)

Part b)

Part c)

Explanation:

Part a)

As we know that final velocity is

angle made by it is given as

now we know its two components are

now we can use kinematics in Y direction

Part b)

Also we know that velocity in x direction will remains same

so

so net speed is given as

Part c)

Angle of projection is given as

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.