a stone dropped from a balloon which was rising at the rate of 15 ft./sec. reached the ground in 8 seconds. how high was the balloon when the stone was dropped?
height of balloon = -16t^2 + 15t + h
0 = -16(8^2) + 15(8) + h
h = .....
it's 904 ft.
thank you :-)
To determine the height of the balloon when the stone was dropped, we can use the following steps:
1. Calculate the total distance the stone traveled during the 8 seconds it took to reach the ground:
Distance = (0.5) * (acceleration due to gravity) * (time^2)
The acceleration due to gravity is approximately 32 ft/sec^2. Therefore:
Distance = (0.5) * (32 ft/sec^2) * (8 sec)^2
Distance = 16 ft/sec^2 * 64 sec^2
Distance = 1024 ft
2. Since the stone was dropped from the balloon, the total distance traveled is the sum of the height of the balloon and the distance it fell. Let's denote the height of the balloon as "h".
Total Distance = Distance the Stone Fell (1024 ft) + Height of the Balloon (h)
3. Since the balloon was rising at a rate of 15 ft/sec, we need to consider the distance the balloon traveled during the 8 seconds it took for the stone to reach the ground:
Distance the Balloon Traveled = (rate of ascent) * (time)
Distance the Balloon Traveled = 15 ft/sec * 8 sec
Distance the Balloon Traveled = 120 ft
4. Substitute the values into the equation from step 2:
1024 ft = 1024 ft (distance the stone fell) + h (height of the balloon)
1024 ft = 1024 ft + 120 ft
1024 ft = 1144 ft + h
5. Solve for the height of the balloon (h):
h = 1024 ft - 1144 ft
h = -120 ft
The negative sign indicates that the balloon was already 120 ft below the starting point when the stone was dropped. Therefore, the height of the balloon when the stone was dropped was 120 ft below the starting point of the stone.