A stone falls from a railroad overpass which is 36 ft high into the path of a train which is approaching the overpass with a uniform speed. If the stone falls when the train is 50 ft away from the overpass and the stone hits the ground just as the train arrives at that spot, how fast is the train moving?
d = Vo*t + 0.5gt^2 = 36 ft.
0 + 0.5*32t^2 = 36,
16t^2 = 36,
t^2 = 2.25,
t = 1.5s.
d = Vt,
V = d / t = 50 / 1.5 = 33.33 Ft / s.
find time to fall.
h=1/2 g t^2 find time. g=32ft/sec^2
Now, the train: d=rt
50ft=v*t
v will be in ft/sec
TUON MO CHOY
To find the speed of the train, we need to determine the time it takes for the stone to fall and hit the ground. Once we have the time, we can calculate the speed of the train using the distance traveled by the train.
First, let's determine the time it takes for the stone to fall. We can use the formula for the time it takes for an object to fall freely under gravity:
time = sqrt((2 * height) / g)
where "height" is the height the stone falls from (in this case, 36 ft), and "g" is the acceleration due to gravity (approximately 32.2 ft/s^2).
Plugging in the values into the formula:
time = sqrt((2 * 36) / 32.2)
= sqrt(72 / 32.2)
= sqrt(2.236)
≈ 1.49 seconds
Now that we have the time, we can calculate the speed of the train. The train covers a distance of 50 ft during this time. So we can use the equation:
speed = distance / time
speed = 50 ft / 1.49 s
≈ 33.56 ft/s
Therefore, the train's speed is approximately 33.56 ft/s.
d = Vo*t + 0.5gt^2 = 36 ft.
0 + 0.5*32t^2 = 36,
16t^2 = 36,
t^2 = 2.25,
t = 1.5s.
d = Vt,
V = d / t = 50 / 1.5 = 33.33 Ft / s.