Answer:
-26 m/s (backward)
Explanation:
We can solve this problem by using the law of conservation of momentum.
In fact, the total momentum momentum of the cannon + ball system must be conserved before and after the explosion.
Before the explosion, they are both at rest, so the total momentum is zero:
p = 0
After the explosion, the total momentum is:

where
M = 1.5 kg is the mass of the cannon
m = 0.52 kg is the mass of the ball
v = +75 m/s is the velocity of the ball
V is the velocity of the cannon
Since the momentum is conserved, we can equate the two expressions:

And solving, we find V:

where the negative sign means the direction is opposite to that of the ball.
Answer:
24 miles
Explanation:
Make a proportion
He is traveling at a constant rate of 12 miles/hour, so
he can go 12 miles in 1 hour, and x miles in 2 hours
12/1=x/2
Multiply both sides by 2
2*12/1=x/2 *2
24=x
So, in 2 hours he can travel 24 miles
To solve this problem it is necessary to apply the kinematic equations of linear and angular motion, as well as the given definitions of the period.
Centripetal acceleration can be found through the relationship

Where
v = Tangential Velocity
R = Radius
At the same time linear velocity can be expressed in terms of angular velocity as

Where,
R = Radius
Angular Velocity
PART A) From this point on, we can use the values used for the period given in the exercise because the angular velocity by definition is described as

T = Period
So replacing we have to

Since 
Then the radius in meters would be


Then the centripetal acceleration would be

From the result obtained, considering that it is an unimaginably low value of an order of less than
it is possible to conclude that it supports the assertion on the inertial reference frame.
Answer:
a) v = 0
b) The aceleration is 1.41 
c) The block is accelerating away from the wall.
Explanation:
First, you need to think about the effect this constant force is causing in the spring: it causes a displacement in the equilibrium point of the system, therefore we need to know where it sits now:
At equilibrium no movement is present reducing friction to 0:




This means that the spring can be compressed with the single force up to 68 cm, Any further compression will cause an unbalanced system and the occilation of the mass.
The spring can't be compressed by the given force to 80 cm, therefore it must have been compressed by another force and then released.
In this case, the instantanous speed is 0, since the block has just been released.
In the same instant we can stimate the free body diagram of forces by the next two equations:

For the y axis:

To calculate the force of friction:

Therefore for x axis:

