A stone dropped from a ballon which was rising at the rate of 15 ft./sec. reached the ground in 8 seconds. how high was the ballon when the stone was dropped?
please help :-) thank you
h = Vo*t + 0.5g*t^2 = -15*8 + 16*8^2 =
-120 + 1024 = 904 Ft.
To solve this problem, we can use the equation of motion for constant acceleration. Here's how you can do it step by step:
1. First, you need to find the initial velocity of the stone when it was dropped. Since the stone was dropped from a balloon that was rising at a rate of 15 ft./sec, the initial velocity of the stone will be -15 ft./sec (negative because it is going downwards).
2. Next, we need to find the total time it took for the stone to reach the ground. In this case, it took 8 seconds.
3. Now, using the equation of motion for constant acceleration, which is given by:
𝑑 = 𝑣₀𝑡 + ½𝑎𝑡²
Where:
𝑑 = distance
𝑣₀ = initial velocity
𝑡 = time
𝑎 = acceleration
Since the stone is dropped vertically downward, the acceleration due to gravity is approximately -32 ft./sec² (negative because it is pointing downwards).
4. Plug in the values into the equation and solve for distance (height in this case):
𝑑 = -15(8) + ½(-32)(8)²
= -120 + ½(-32)(64)
= -120 + (-512)
= -120 - 512
= -632 ft.
The negative sign indicates that the height is below the starting point (the balloon).
Therefore, the balloon was approximately 632 ft. above the ground when the stone was dropped.