1. A-20 km south east
The car's displacement consists of two components into two different directions. Using a system of coordinates in which x represents the east direction and y represents the south direction, the two displacements are:
east
south
Since the two components are orthogonal to each other, we can find the resultant displacement by using Pythagorean's theorem:
![d=\sqrt{d_x^2+d_y^2}=\sqrt{(12 km)^2+(16 km)^2}=\sqrt{400}=20 km](https://tex.z-dn.net/?f=d%3D%5Csqrt%7Bd_x%5E2%2Bd_y%5E2%7D%3D%5Csqrt%7B%2812%20km%29%5E2%2B%2816%20km%29%5E2%7D%3D%5Csqrt%7B400%7D%3D20%20km)
and the direction is between the two original directions, so south-east.
2. D. 10 m/s
First of all, we need to calculate the total time the stone took to hit the ground. Since the vertical distance covered is S = 78.4 m, and since the motion is an accelerated motion with constant acceleration g=9.8 m/s^2, we have
![S=\frac{1}{2}gt^2](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
From which we find the total time of the fall, t:
![t=\sqrt{\frac{2S}{g}}=\sqrt{\frac{2(78.4 m)}{9.8 m/s^2}}=4 s](https://tex.z-dn.net/?f=t%3D%5Csqrt%7B%5Cfrac%7B2S%7D%7Bg%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%2878.4%20m%29%7D%7B9.8%20m%2Fs%5E2%7D%7D%3D4%20s)
Now we can consider the horizontal motion of the stone: we know that the stone travels for d = 40 m in a time of t = 4 s, therefore the horizontal velocity of the stone is
![v=\frac{d}{t}=\frac{40 m}{4 s}=10 m/s](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D%3D%5Cfrac%7B40%20m%7D%7B4%20s%7D%3D10%20m%2Fs)
3. B=32.32 m
As in the previous problem, we have to calculate the total time it takes for the stone to reach the river first. Since the vertical distance covered is S = 20 m, we have
![t=\sqrt{\frac{2S}{g}}=\sqrt{\frac{2(20 m)}{9.8 m/s^2}}=2.0 s](https://tex.z-dn.net/?f=t%3D%5Csqrt%7B%5Cfrac%7B2S%7D%7Bg%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%2820%20m%29%7D%7B9.8%20m%2Fs%5E2%7D%7D%3D2.0%20s)
And since the stone is traveling horizontally at v = 16 m/s, the horizontal distance covered is
![d=vt=(16 m/s)(2 s)=32 m](https://tex.z-dn.net/?f=d%3Dvt%3D%2816%20m%2Fs%29%282%20s%29%3D32%20m)
So, the closest answer is B.