<span>31.3 m/s
Since the water balloon is being launched at a 45 degree angle, the horizontal and vertical speeds will be identical. Also the time the balloon takes to reach its peak altitude will match the time it takes to fall. So let's create a few expressions about what we know.
Distance the water balloon travels at velocity v for time t
d = vt
Total time required for the entire trip is double since the balloon goes up, then goes down
t = 2v/a
Now let's plug in the numbers we have, assuming the acceleration due to gravity is 9.8 m/s^2
t = 2v/9.8
100 = vt
Substitute 2v/9.8 for t in the 2nd formula
100 = v(2v/9.8)
Solve for v.
100 = v(2v/9.8)
100 = 2v^2/9.8
980. = 2v^2
490 = v^2
22.13594 = v
So we now know that both the horizontal velocity and vertical velocity needed is 22.13594 m/s. Let's verify that
2*22.13594 / 9.8 = 4.51754
So it will take 4.51754 second for the balloon to hit the ground after being launched.
4.51754 * 22.13594 = 100
And during that time it will travel 100 meters horizontally.
But we need to know the total velocity. And the Pythagorean theorem comes to the rescue. Just square the 2 velocities, add them together, and take the square root. We already know the square is 490 from the work above, so
sqrt(490+490) = sqrt(980) = 31.30495 m/s</span>
Answer:
Flow rate 2.34 m3/s
Diameter 0.754 m
Explanation:
Assuming steady flow, the volume flow rate along the pipe will always be constant, and equals to the product of flow speed and cross-section area.
The area at the well head is
So the volume flow rate along the pipe is
We can use the similar logic to find the cross-section area at the refinery
The radius of the pipe at the refinery is:
So the diameter is twice the radius = 0.38*2 = 0.754m
Phonograph. Hope that helps
Answer:
52 mm/s (approximately)
Explanation:
Given:
Initial speed of the projectile is,
Angle of projection is,
Time taken to land on the hill is,
In a projectile motion, there is acceleration only in the vertical direction which is equal to acceleration due to gravity acting vertically downward. There is no acceleration in the horizontal direction.
So, the velocity in the horizontal direction always remains the same.
The horizontal component of initial velocity is given as:
Now, the velocity in the vertical direction goes on decreasing and becomes 0 at the highest point of the trajectory. So, at the highest point, only horizontal component acts.
Therefore, the projectile's velocity at the highest point of its trajectory is equal to the horizontal component of initial velocity and thus is equal to 52 mm/s.
Answer:
a) 3.43 m/s
Explanation:
Due to the law of conservation of momentum, the total momentum of the bullet - rifle system must be conserved.
The total momentum before the bullet is shot is zero, because they are both at rest, so:
Instead the total momentum of the system after the shot is:
where:
m = 0.006 kg is the mass of the bullet
M = 1.4 kg is the mass of the rifle
v = 800 m/s is the velocity of the bullet
V is the recoil velocity of the rifle
The total momentum is conserved, therefore we can write:
Which means:
Solving for V, we can find the recoil velocity of the rifle:
where the negative sign indicates that the velocity is opposite to direction of the bullet: so the recoil speed is
a) 3.43 m/s