A 40 lb missile moves with a velocity of 150 ft/sec. It is intercepted by a laser beam which causes it to
explode into two fragments A and B which weigh 25 lb and 15 lb, respectively. If the fragments A and B
travel 45 degrees counter-clockwise from horizontal and30 degrees clockwise from horizontal,
immediately after explosion, find the magnitude of velocity of fragment A.
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A 40 lb missile moves horizontally with a velocity of 150 ft/s. It is intercepted by a laser beam, which causes it to explode into two fragments A and B, which weigh 25 lbs and 15 lbs, respectively. If A travels at an angle of 45 degrees from the horizontal while B travels at 30 degrees from the horizontal immediately after the explosion, find the magnitude of the velocity of fragment A.
Well, this is quite an explosive question! Let's break it down, shall we?
First, we need to find the total momentum before and after the explosion. The total momentum before the explosion can be calculated by multiplying the mass of the missile by its velocity. So, the momentum before the explosion is 40 lb * 150 ft/sec.
Now, after the explosion, the missile breaks into two fragments, A and B, with weights of 25 lb and 15 lb, respectively. To find the magnitude of the velocity of fragment A, we'll have to consider the conservation of momentum.
Since the fragments travel in different directions, we need to break down the momentum into vertical and horizontal components. Fragment A travels at 45 degrees counterclockwise from the horizontal, so its horizontal component of momentum would be 25 lb * the cosine of 45 degrees, and its vertical component would be 25 lb * the sine of 45 degrees.
Similarly, fragment B travels at 30 degrees clockwise from the horizontal, so its horizontal component of momentum would be 15 lb * the cosine of 30 degrees, and its vertical component would be 15 lb * the sine of 30 degrees.
To calculate the magnitude of the velocity of fragment A, we can use the Pythagorean theorem. The magnitude of the velocity of fragment A would be the square root of the sum of the squares of its horizontal and vertical components.
Now, comes the fun part of math. But hey, since I'm a clown bot, I'll just give you an answer straight from clown school: The magnitude of the velocity of fragment A is... drumroll, please... "Zooming-and-booming" ft/sec! So, put on your clown shoes and let the explosions roll!
To find the magnitude of velocity of fragment A, we need to use the concept of conservation of momentum. According to the law of conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion.
To begin, we need to find the initial momentum of the missile before the explosion. The momentum of an object is calculated by multiplying its mass (m) by its velocity (v). So, the initial momentum of the missile can be calculated as:
Initial momentum of the missile = mass of missile * velocity of missile
Given:
Mass of missile = 40 lb
Velocity of missile = 150 ft/sec
Substituting these values, we can find the initial momentum of the missile.
Next, we need to find the total momentum after the explosion. Since the missile breaks into two fragments, we need to calculate the momentum of each fragment separately.
To find the momentum of a fragment, we can use the formula:
Momentum of a fragment = mass of the fragment * velocity of the fragment
Given:
Mass of fragment A = 25 lb
Mass of fragment B = 15 lb
Now, we need to find the velocities of fragments A and B. We are provided with the angles at which they travel immediately after the explosion.
To find the magnitude of velocity of fragment A, we can use trigonometry. The horizontal component of velocity will be the velocity of fragment A multiplied by the cosine of the angle (45 degrees counter-clockwise from horizontal). Similarly, the vertical component of velocity will be the velocity of fragment A multiplied by the sine of the angle.
Once we have the horizontal and vertical components of velocity of fragment A, we can calculate the magnitude of velocity using the Pythagorean theorem:
Magnitude of velocity of fragment A = sqrt((horizontal component)^2 + (vertical component)^2)
By substituting the known values and using the above calculations, we can find the magnitude of velocity of fragment A.
A 40 lb missile horizontally with a velocity of 150 ft/s. it is intercepted by a laser beam, which causes it to explode into two
fragments A and B, which weigh 25 lbs and 15 lbs, respectively. If a travels at an angle of 45 degrees from the horizontal while B
travels at 30 degrees from the horizontal immediately after the explosion, find the magnitude of velocity of fragment A.