Refer to the diagram shown below.
Define the (x,y) plane as the horizontal plane of the floor.
There was no momentum in the (x,y) plane before the plate hit the floor.
Let the velocity components in the (x) and (y) directions of the 100 g mass be Vx and Vy respectively, and that the resultant velocity, V, makes an angle θ below the negative x-axis as shown.
Because momentum is conserved, therefore
100*Vx + 320*2 = 0
100Vx = -640
Vx = -6.4 m/s
100Vy + 355*1.5 = 0
100Vy = -532.5
Vy = -5.325 m/s
V = √[(-6.4)² + (-5.325)²] = 8.33 m/s
θ = tan⁻¹ (-5.325/-6.4) = 39.8°
Answer:
The direction is 39.8° below the negative x-axis
The speed is 8.33 m/s
Answer:
80mm or 8cm
Explanation:
According to the lens formula,
1/f = 1/u+1/v
If the object distance u = 4cm = 40mm
Object height = 1.5mm
Image height = 3mm
First, we need to get the image distance (v) using the magnification formula Magnification = image distance/object distance = Image height/object height
v/40=3/1.5
1.5v = 120
v = 120/1.5
v = 80mm
The image distance is 80mm
To get the focal length, we will substitute the image distance and the object distance in the mirror formula to have;
1/f = 1/40+1/-80
Note that the image formed by the lens is an upright image (virtual), therefore the image distance will be negative.
Also the focal length of the converging lens is positive. Our formula will become;
1/f = 1/40-1/80
1/f = 2-1/80
1/f = 1/80
f = 80mm
The focal length of the lens 80mm or 8cm
Answer:
F = 20.4 i ^
Explanation:
This exercise can be solved using the ratio of momentum and amount of movement.
I = F t = Dp
Since force and amount of movement are vector quantities, each axis must be worked separately.
X axis
Let's look for speed
cos 45 = vₓ / v
vₓ = v cos 45
vₓ = 8 cos 45
vₓ = 5,657 m / s
We write the moment
Before the crash p₀ = m vₓ
After the shock 
= -m vₓ
The variation of the moment Δp = mvₓ - (-mvₓ) = 2 m vₓ
The impulse on the x axis Fₓ t = Δp
Fₓ = 2 m vₓ / t
Fx = 2 0.450 5.657 / 0.250
Fx = 20.4 N
We perform the same calculation on the y axis
sin 45 = vy / v
vy = v sin 45
vy = 8 sin 45
vy = 5,657 m / s
We calculate the initial momentum po = m 
Final moment = m
Variations moment Δp = m - m = 0
Force in the Y-axis 
= 0
Therefore the total force is
F = fx i ^ + Fyj ^
F = Fx i ^
F = 20.4 i ^
<span>Since the trains area headed in completely opposite directions, the rate at which they gain distance from each other is simply equal to the sum of the magnitudes of their velocities, in this case 85 + 75 = 160 miles per hour. Therefore, the amount of time it will take for them to be 352 miles apart is 352/160 = 2.2 hours, or 2 hours and 12 minutes.</span>
