Two blocks, of mass m and 2m, are initially at rest on a horizontal frictionless surface. A force F is exerted individually on e
1 answer:
You might be interested in
Answer:
(a) 196 m/s
(b) 490 m
(c) 3394.82 m
(d) 2572.5 m
Explanation:
First of all, let us know one thing. When an object is thrown in the air, it experiences two forces acting in two different directions, one in the horizontal direction called air resistance and the second in the vertically downward direction due to its weight. In most of the cases, while solving numerical problems, air resistance is neglected unless stated in the numerical problem. This means we can assume zero acceleration along the horizontal direction.
Now, while solving our numerical problem, we will discuss motion along two axes according to our convenience in the course of solving this problem.
<u>Given:</u>
- Time of flight = t = 20 s
- Angle of the initial velocity of projectile with the horizontal =
<u>Assume:</u>
- Initial velocity of the projectile = u
- R = Range of the projectile during the time of flight
- H = maximum height of the projectile
- D = displacement of the projectile from the initial position at t = 15 s
Let us assume that the position from where the projectile was projected lies at origin.
- Initial horizontal velocity of the projectile =
- Initial horizontal velocity of the projectile =
Part (a):
During the time of flight the displacement of the projectile along the vertical is zero as it comes to the same vertical height from where it was projected.
Hence, the initial speed of the projectile is 196 m/s.
Part (b):
For a projectile, the time take by it to reach its maximum height is equal to return from the maximum height to its initial height is the same.
So, time taken to reach its maximum height will be equal to 10 s.
And during the upward motion of this time interval, the distance travel along the vertical will give us maximum height.
Hence, the maximum altitude is 490 m.
Part (c):
Range is the horizontal displacement of the projectile from the initial position. As acceleration is zero along the horizontal, the projectile is in uniform motion along the horizontal direction.
So, the range is given by:
Hence, the range of the projectile is 3394.82 m.
Part (d):
In order to calculate the displacement of the projectile from its initial position, we first will have to find out the height of the projectile and its range during 15 s.
Hence, the displacement from the point of launch to the position on its trajectory at 15 s is 2572.5 m.
Answer:
a
b
The value is
Explanation:
From the question we are told that
The mass is
The spring constant is
The instantaneous speed is
The position consider is x = 0.750A meters from equilibrium point
Generally from the law of energy conservation we have that
The kinetic energy induced by the hammer = The energy stored in the spring
So
Here a is the amplitude of the subsequent oscillations
=>
=>
=>
Generally from the law of energy conservation we have that
The kinetic energy by the hammer = The energy stored in the spring at the point considered + The kinetic energy at the considered point
=>
=>