A missile of mass 1.20 102 kg is fired from a plane of mass 5.10 103 kg initially moving at a speed of 3.35 102 m/s. If the speed of the missile relative to the plane is 1.21 103 m/s, what is the final velocity of the plane? HELP I have no idea how to do this
When expression exponents, please precede the exponent by the ^ sign.
For example, 10² should be written as 10^2.
102 means one hundred and two, (write 10^2)
103 means one hundred and three, (write 10^3)
Confusions will arise if the numbers are not expressed correctly.
with newton 2nd law:when the jet release gas,impulse created result in an increase in the jet'svelocity:ft=mv=1.201*1.2103=1.454N/s 1.454=5.101(v-3.351) 0.285=v-3.351 v=3.636m/s
To solve this problem, we can use the principle of conservation of linear momentum. According to this principle, the total linear momentum of an isolated system remains constant if no external forces act on it.
The linear momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v): p = m * v.
Let's denote the initial velocity of the plane as v_p, the final velocity of the plane as v_pf, the initial velocity of the missile as v_m, the final velocity of the missile as v_mf, the mass of the plane as m_p, and the mass of the missile as m_m.
We are given the following information:
Initial velocity of the plane, v_p = 3.35 * 10^2 m/s
Mass of the plane, m_p = 5.10 * 10^3 kg
Mass of the missile, m_m = 1.20 * 10^2 kg
Speed of the missile relative to the plane, v_mf - v_p = 1.21 * 10^3 m/s (Note: We subtract v_p because velocities are vectors and we want the relative velocity between the missile and the plane.)
Using the conservation of linear momentum, we can write the equation for the initial momentum equaling the final momentum:
(m_p * v_p) + (m_m * v_m) = (m_p * v_pf) + (m_m * v_mf)
We need to solve for v_pf, the final velocity of the plane. To do that, let's rearrange the equation:
v_pf = [(m_p * v_p) + (m_m * v_m) - (m_m * v_mf)] / m_p
Now we can substitute the known values into the equation and perform the calculation:
v_pf = [(5.10 * 10^3 kg * 3.35 * 10^2 m/s) + (1.20 * 10^2 kg * 3.35 * 10^2 m/s) - (1.20 * 10^2 kg * 1.21 * 10^3 m/s)] / (5.10 * 10^3 kg)
By calculating this expression, you will find the final velocity of the plane, v_pf.