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 reach the edge of a 4.2 m waterfall. If the spy's speed is 20 m/s and the officials' speed is 24 m/s, how far apart will the two vessels be when they land below the waterfall?
h = Vo*t + 0.5g*t^2 = 4.2 m.
20t + 4.9t^2 = 4.2
4.9t^2 + 20t - 4.2 = 0
Use Quad. formula.
t1 = 0.200 s. = The spy's time.
24t + 4.9t^2 -4.2 = 0
4.9t^2 + 24t - 4.2 = 0
t2 = 0.169 s. = Gov. officials' time.
t1-t2 = 0.200 - 0.169 = 0.031 s. apart.
Correction: See recent post: Tue, 9-12-14, 11:13 AM.
Well, this is quite a watery situation we have here! Let's see if we can splash some humor into the calculations.
First things first, we need to find out how much time it takes for both the spy's boat and the officials' boat to reach the edge of the waterfall. Since the distance is the same for both boats, we can use the formula: distance = speed * time.
For the spy's boat: 4.2 m = 20 m/s * time
And for the official's boat: 4.2 m = 24 m/s * time
Now, let's solve those equations using our trusty algebra skills. After some calculations, we find that the time taken for both boats to reach the edge of the waterfall is 0.21 seconds.
But wait, it's not over yet! We still need to find out the distance between the two boats when they land below the waterfall. Since both boats have been traveling at a constant speed, the distance between them remains the same throughout.
So, multiplying the time by the relative speed of the two boats (24 m/s - 20 m/s = 4 m/s), we get the distance between the two boats when they land below the waterfall:
0.21 seconds * 4 m/s = 0.84 meters.
Voila! The spy and the officials will be 0.84 meters apart when they make their daring descent. Let's hope they don't make too big of a splash!
To find the distance between the two vessels when they land below the waterfall, we need to calculate the time it takes for both vessels to reach the bottom of the waterfall.
Step 1: Calculate the time taken for the spy's boat to reach the bottom of the waterfall.
The distance traveled by the spy's boat is equal to the product of its speed and time taken: d = v * t
Given:
Speed of the spy's boat (v_spy) = 20 m/s
Distance traveled by the spy's boat (d_spy) = 4.2 m
Rearranging the formula, we can find the time taken by the spy's boat: t_spy = d_spy / v_spy
Substituting the values, we get: t_spy = 4.2 m / 20 m/s = 0.21 s
Step 2: Calculate the time taken for the officials' boat to reach the bottom of the waterfall.
Using the same approach as step 1, we can calculate the time taken by the officials' boat.
Speed of the officials' boat (v_officials) = 24 m/s
Distance traveled by the officials' boat (d_officials) = 4.2 m
t_officials = d_officials / v_officials
t_officials = 4.2 m / 24 m/s = 0.175 s
Step 3: Find the distance between the two vessels when they land below the waterfall.
Since both vessels start at the same point and reach the bottom of the waterfall at different times, we can calculate the distance between them based on the time difference.
Δt = t_officials - t_spy
Δt = 0.175 s - 0.21 s = -0.035 s (negative value indicates the spy's boat reached the bottom first)
To find the distance between the two vessels, we use the formula: distance = speed * time
distance = v_officials * Δt
distance = 24 m/s * (-0.035 s)
distance = -0.84 m
The negative sign indicates that the spy's boat will be 0.84 meters in front of the officials' boat when they land below the waterfall. However, since distance cannot be negative in this context, we consider the vessels to be approximately 0 meters apart when they land below the waterfall.