1-a car moves toward east 12km is represented as a and it turns towards south 16km is represented as b. what is the resultant vector of a-b
a-20 km south east
b-25 km south east
c-20km north east
d-25 km north east

2-a stone is thrown horizontally from the top of a tower of height 78.4 m. it reaches 40 m away from the foot of the tower. what is its initial velocity of projection?
h=1/2gt^2
x=vx^2
a=2.5 m/s
b=5 m/s
c=7.5 m/s
d=10 m/s

a storm is projected horizontally with a velocity of 16 m/s from the bridge at a height of 20 m from the river. how far away (x) parentheses from the bridge is the stone when it reaches the river
h= 1/2gt^2
x=vx^2
a= 36 m
b=32.32 m
c=4m
d=24.23 m

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:

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

From which we find the total time of the fall, t:

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

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

And since the stone is traveling horizontally at v = 16 m/s, the horizontal distance covered is

So, the closest answer is B.

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.