Answer:
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Explanation:
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Use the formula distance = rate * time. substitute in the values you know, which gives you distance = 120mph * 3.5hours. multiply 120 and 3.5 to get distance = 420 miles.
Answer:
The displacement is 6.71 [m} and the angle is 63.4° to the north of east
Explanation:
Using a sketch showing Dante's displacement, we can find each of the points Dante moves through. First, it moves 4 blocks east, the new coordinate (4.0), then moves 3 blocks south and we will get the new coordinate (4, -3). Then Dante moves 1 block west, thus the new point is (3, -3). And finally it moves 9 blocks north where the new coordinate in and gets -3 - (-9) = + 6.
The displacement can be found using the equation for the straight line.
![d= \sqrt{(x_{1}-x_{0} )^{2} +(y_{1}-y_{0} )^{2} } \\d= \sqrt{(3-0 )^{2} +(6-0 )^{2} } \\\\d=6.71 [m]\\](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28x_%7B1%7D-x_%7B0%7D%20%29%5E%7B2%7D%20%2B%28y_%7B1%7D-y_%7B0%7D%20%29%5E%7B2%7D%20%7D%20%5C%5Cd%3D%20%5Csqrt%7B%283-0%20%29%5E%7B2%7D%20%2B%286-0%20%29%5E%7B2%7D%20%7D%20%5C%5C%5C%5Cd%3D6.71%20%5Bm%5D%5C%5C)
We can realize that the triangle formed is a right triangle, therefore we can find the angle of the displacement.
![tan(a)=\frac{6}{3} \\a=tan^-1(2)\\a=63.4[deg]](https://tex.z-dn.net/?f=tan%28a%29%3D%5Cfrac%7B6%7D%7B3%7D%20%5C%5Ca%3Dtan%5E-1%282%29%5C%5Ca%3D63.4%5Bdeg%5D)
Explanation:
Use the height of the cliff to determine how long it took the car to land.
Take down to be positive. Given:
Δy = 7.93 m
v₀ = 0 m/s
a = 9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
7.93 m = (0 m/s) t + ½ (9.8 m/s²) t²
t = 1.27 s
Use the time to calculate the horizontal velocity.
Given:
Δx = 26.7 m
a = 0 m/s²
Find: v₀
Δx = v₀ t + ½ at²
26.7 m = v₀ (1.27 s) + ½ (0 m/s²) (1.27 s)²
v₀ = 21.0 m/s
The driver was going 21.0 m/s, faster than the speed limit of 9.72 m/s.