A hot air balloon containing an AP Physics student ascends vertically at a constant speed of 8 m/s. While ascending, he accidentally drops his rubber duckie from the gondola of the ballong. Seven seconds after it is dropped the duckie bounces off a roof at point A and hits the ground at point B as shown in the sketch at the right.

A. Find the distance from the point where the duckie is dropped to point A
B. Find the speed of the sweet little rubber duckie just before it hits the roof

Suppose that immediately after bouncing off the roof, the velocity of the rubber duckie is 12m/s 37 degrees BELOW the horizontal and that point B is horizontal distance of 24 meters from point A.

C. Find how far point A is above point B
D. Find the duckie's time of flight between points A and B
E. Find the Velocity of the duckie the instant before it strikes the ground at Point B

My ans:
A. 240 meters
B. 68.6 meters
C. 49 meters
D. 2.51 seconds
E. 31.8 meters per second

To find the answers to the given questions, we need to use the equations of motion and kinematics. Let's break down each question and explain how to arrive at the answers.

A. Finding the distance from the point where the duckie is dropped to point A:
Since the duckie is dropped from the hot air balloon, it will have the same vertical velocity as the balloon, which is 8 m/s. It takes 7 seconds for the duckie to reach point A. Therefore, the distance traveled vertically is given by the formula: distance = velocity * time.
Distance = 8 m/s * 7 s = 56 meters

B. Finding the speed of the duckie just before it hits the roof:
We are given the velocity immediately after the duckie bounces off the roof, which is 12 m/s at an angle of 37 degrees below the horizontal. To find the speed just before it hits the roof, we can use the horizontal component of the velocity. The horizontal component is given by speed * cosine(angle).
Speed = 12 m/s * cosine(37 degrees) = 9.6 m/s

C. Finding how far point A is above point B:
We are given that point B is a horizontal distance of 24 meters away from point A. Since the balloon is ascending vertically at a constant speed, the horizontal distance will remain the same. Therefore, the difference in height between point A and point B is the same as the vertical distance traveled by the duckie.
Height difference = Distance from point A to point B = 56 meters

D. Finding the duckie's time of flight between points A and B:
The time of flight can be calculated using the vertical velocity and the height difference. We can use the formula: time = distance / velocity.
Time = 56 meters / 8 m/s = 7 seconds

E. Finding the velocity of the duckie the instant before it strikes the ground at point B:
To find the velocity of the duckie just before it hits the ground, we need to calculate the vertical component of the velocity. The duckie will continue to have the same vertical velocity throughout its flight. Therefore, the vertical component of velocity is -8 m/s (negative because it is moving downward).
Velocity = -8 m/s

Please note that the values provided are based on the given information and calculations.