A spy in a speed boat is being chased down a river by government officials in a faster craft. Just as the officials' boat pulls up next to the spy's boat, both boats reach the edge of a 4.8 m waterfall. The spy's speed is 16 m/s and the officials; speed is 26 m/s. How far apart will the two vessels be when they land below the waterfall? The acceleration of gravity is 9.81 m/s . Answer in units of m
how long does it take to fall 4.8m?
d= 1/2 g t^2
4.8=4.8t^2 t=1sec
so now the boats distance apart is relative speed*time= 10m/s*1s=10m
To find the distance between the two vessels when they land below the waterfall, we need to determine the time it takes for each boat to reach the bottom after they go over the waterfall.
Let's first calculate the time it takes for the spy's boat to reach the bottom of the waterfall. We can use the equation:
h = (1/2)gt^2
where h is the height of the waterfall (4.8 m), g is the acceleration due to gravity (9.81 m/s^2), and t is the time.
Plugging in the values, we have:
4.8 = (1/2)(9.81)(t^2)
Simplifying the equation:
4.8 = 4.905t^2
Dividing both sides by 4.905:
t^2 = 0.979
Taking the square root of both sides:
t ≈ 0.99 seconds
Now, let's calculate the time it takes for the officials' boat to reach the bottom of the waterfall. Since they are traveling faster, the time will be slightly less. We can use the same equation:
4.8 = 4.905t^2
Simplifying the equation:
4.8 = 4.905t^2
Dividing both sides by 4.905:
t^2 = 0.979
Taking the square root of both sides:
t ≈ 0.99 seconds
So both boats will take approximately 0.99 seconds to reach the bottom of the waterfall.
Now, let's calculate the distance traveled by each boat during this time. We can use the equation:
d = vt
where d is the distance, v is the velocity, and t is the time.
For the spy's boat:
distance = 16 m/s * 0.99 s = 15.84 m
For the officials' boat:
distance = 26 m/s * 0.99 s = 25.74 m
Therefore, when they land below the waterfall, the two vessels will be approximately 15.84 meters apart.