A10 kg projectile is fired from a cannon at an angle of 60^ above the horizontal and with an initial velocity of 300 m/s. at the highest point of its flight, the projectile explodes into two fragments with equal mass. one of the fragments falls vertically downwards with an initial velocity of zero.

question 1: how far from the cannon does the other fragment strike the ground( assume the ground is level)?

question 2: how much energy is released during the explosion?

Question 1, answer = 7950[m]. Question 2, answer = 394250 [J]

Explanation:

There are certain conditions of this problem, which can simplify its solution, the first condition is that when the ball reaches the highest point its velocity in the y- axis component and is zero, in this way we can use the following kinematic equation for parabolic motion.

But first let's decompose the initial velocity into x & y

Now replacing the values:

With this time and the next equation, we can find the highest point of the trajectory

Now we have the highest point, so we can find the potential energy, which will be useful for solving question 2.

For solving question 1, we need to find the time when one of the fragments is on the ground, therefore.

Now using this time for the movement in the x-axis.

The total amount of energy due explosion will be equal to the sum of the energies at that precise moment.

The above equation tells us that the energy of the explosion is equal to the sum of the potential and kinetic energies of both fragments.

Let us remember that both fragments are of equal mass.

Fragment 1

The kinetic energy for the fragment 1 is zero, because it falls downwards with an initial velocity of zero.

Fragment 2

Now for the kinetic energy we will use the velocity calculated v = 150 [m/s], this is the velocity of the fragment 2 in the x-axis.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y