please explain how solve it. A hot air ballon rises straight up with a constant

Question

please explain how solve it. A hot air ballon rises straight up with a constant speed of 7m/s^2 j hat. When the basket of the ballon's position vector is (50 m) j hat above the ground, one of the passengers opens a champagne bottle, expelling the cork with an initial velocity vector of 4 m/s i hat. Assume the champagne cork has the same position vector as the basket initially: initial vector r (t=0) = 50 m j hat. Neglect air resistance. a. A stationary person on the ground sees the cork having two motion when expelled from the bottle: the cork ascending and moving horizontally. What is the cork's initial velocity vector as seen by someone standing on the ground? Use the i hat, j hat notation. b. Once the cork is expelled, assume it only experiences acceleration due to gravity. What is the cork's acceleration vector? use the i hat, j hat notation. c. Write final r vector in terms of initial r vector, initial vector v*t and vector a*t^2. d. What is the cork's initial speed as seen by someone standing on the ground? e. what is the cork's initial direction of motion (launch angle relative to a horizontal line) as seen by someone standing on the ground? f. what is the maximum height above the ground attained by the cork? g. What is the cork's position vector when at maximum height? use the i hat and j hat notation. h. What is the cork's velocity vector when at maximum height? Use the i hat and j hat notation. i. What is the postion vector where the cork lands? Use the i hat and j hat notation. j. What is the cork's velocity vector when the cork lands? use the i hat jhat notation. k. What is the cork's speed when the cork lands? l. What is the cork's impact angle, measured with respect to the positive x-axis.

Explanation / Answer

initial velocity vector as seen by someone standing on the ground

4 m/s i hat + 7m/s j hat

cork's acceleration vector:

- g j hat

final r vector:

v*t i hat + vt + a*t^2. j hat

cork's initial speed as seen by someone standing on the ground

sqrt(16+49)

= 8.06

initial direction of motion

tan( theta ) = 7/4

theta= 60.25

maximum height above the ground attained by the cork:

50+ 7*7/2g

52.5 m

velocity vector when at maximum height:

v*t i hat

= 2.85 i hat

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