Answer:
2000 kg m/s
Explanation:
The momentum of an object is a vector quantity whose magnitude is given by
where
m is the mass of the object
v is the velocity of the object
and its direction is the same as the velocity.
In this problem, we have:
- Spaceship 1 has
m = 200 kg (mass)
v = 0 m/s (zero velocity)
So its momentum is
- Spaceship 2 has
m = 200 kg (mass)
v = 10 m/s (velocity)
So its momentum is
Therefore, the combined momentum of the two spaceships is
Answer:
Spring constant, k = 283.33 N/m
Explanation:
Given that,
Force acting on the spring, F = 8.5 N
Stretching in the spring, x = 3 cm = 0.03 m
Let k is the spring constant of the spring. It can be calculated using Hooke's law as :
k = 283.33 N/m
So, the spring constant of the spring is 283.33 N/m. Hence, this is the required solution.
Answer:
The height above the waterline that the stream reaches at the horizontal position of the insect is 15 cm.
Explanation:
Please, see the attached figure for a description of the problem.
The motion is parabolic and this is the equation that describes the position of an object in such a motion:
r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)
Where:
r = position vector
x0 = initial horizontal position
v0 = initial velocity
t = time
α = angle of the stream with the waterline
y0 = initial vertical position
g = acceleration due to gravity
First, let´s calculate how much time it takes the stream to reach the horizontal position of 0.27 m. For this, we will use the equation of the x-component of the vector position:
x = x0 + v0 · t · cos α
Since the origin of the reference system is located at the mouth of the fish, x0 = 0. Then:
0.27 m = 3.7 m/s · t · cos 35º
t = 0.27 m /(3.7 m/s · cos 35º)
t = 0.089 s
Now, with this time, we can calulate the vertical position (height) of the stream using the equation for the y-component of the vector "r":
y = y0 + v0 · t · sin α + 1/2 · g · t²
y = 0 m + 3.7 m/s · 0.089 s · sin 35º + 1/2 · (-9.8 m/s²) · (0.089s)²
y = 0.15 m
when the stream reaches 27 cm horizontally, it will reach 15 cm vertically and hit the insect!
