A Balloon carrying a basket is descending at a constant velocity of 20.0 m/s. A person in the basket throws a stone with an initial velocity of 15.0 m/s horizontally perpendicular to the path of descending balloon and 4.00 (s) later this person sees the stone strike the ground.
A) How high was the balloon when the stone was thrown out?
B) How far horizontally does the stone travel before it hits the ground?
C) At the instant the stone hits the ground, how far is it from the basket?
u = 15 forever
Vi = -20
h = Hi + Vi t + (1/2) a t^2
0 = Hi - 20 t - 4.9 t^2
but t = 4
so solve for Hi, initial height
in 4 seconds at 15 goes 60 meters
where is the basket at 4 seconds?
h basket = Hi - 80
d = sqrt (60^2 + h basket^2)
is your d = square root of (60^2 + h basket^2) and for which question a,b or c
To solve this problem, we can break it down into several steps. Let's tackle each question one by one:
A) To determine the height of the balloon when the stone was thrown out, we need to find the time it took for the stone to reach the ground after being thrown. Then we can use that time to calculate the vertical distance traveled by the balloon.
First, we know that the stone was initially launched with a horizontal velocity of 15.0 m/s. Since the vertical velocity is not given, we can assume that there is no acceleration in the vertical direction.
Given:
Initial vertical velocity (u_r) = 0 m/s
Final vertical velocity (v_r) = ?
Time (t) = 4.00 s
Using the equation v_r = u_r + g*t, where g is the acceleration due to gravity (approximately 9.8 m/s²), we can find the final vertical velocity:
v_r = u_r + g*t
v_r = 0 + (9.8 * 4.00)
v_r = 39.2 m/s
Now, to determine the height of the balloon when the stone was thrown out, we need to find the vertical distance traveled by the balloon in 4.00 seconds. Since the balloon is descending at a constant velocity of 20.0 m/s, the vertical distance traveled by the balloon is given by:
Vertical distance = velocity * time
Vertical distance = 20.0 * 4.00
Vertical distance = 80.0 meters
Therefore, the balloon was 80.0 meters high when the stone was thrown out.
B) To find the horizontal distance traveled by the stone before it hits the ground, we need to determine the time it takes for the stone to reach the ground.
Since there is no acceleration horizontally, the horizontal velocity of the stone remains constant throughout its motion. Therefore, the horizontal distance covered by the stone is given by:
Horizontal distance = horizontal velocity * time
Given:
Horizontal velocity (u_h) = 15.0 m/s
Time (t) = ?
To find the time (t), we can use the fact that both the time of flight of the stone in the horizontal direction and the vertical direction are the same. So, we take the time calculated earlier, which is 4.00 seconds.
Therefore, the horizontal distance covered by the stone is:
Horizontal distance = 15.0 * 4.00
Horizontal distance = 60.0 meters
So, the stone travels 60.0 meters horizontally before it hits the ground.
C) At the instant the stone hits the ground, the stone is horizontally away from the basket by the same distance that the basket has descended vertically during the stone's flight time.
We already know that the time taken by the stone to hit the ground is 4.00 seconds. During this time, the balloon has descended vertically at a constant velocity of 20.0 m/s. Therefore, the horizontal distance between the stone and the basket at the instant the stone hits the ground is:
Horizontal distance = velocity * time
Horizontal distance = 20.0 * 4.00
Horizontal distance = 80.0 meters
Thus, at the instant the stone hits the ground, it is 80.0 meters horizontally away from the basket.