Kinematics - relative velocity

Question

A Russian Radar spotted a friendly SU-35 fighter returning home which is located at coordinates (60,30,5)km towards an airfield which is located (0,15,1)km If the SU-35 flies at mach 1.3 as it is low on fuel to the airfield. At the same instant it also spots an enemy Mig -29 km flying towards the Russian Su-35 at mach 1.7 at the same direction as to the Russian Su-35 relatively 7km away from the Su-35. If a Russian S-400 is at the said airfield ready to launch Anti-Air missiles that can cruise at mach 3.5.

If there is a delay of 5 seconds due to transmission distance. Note: Intercept missions are movements on straight line to reach the target at gun point distances 600meters

Find the Total Time for the Missile to hit the enemy fighter If it launched at the airfield.

If the base was not alerted by the radar and if the enemy Mig – 29 launches Air – to –air missiles speeding at mach 2.7. find the distance travelled by the missile.

Find the relative velocity of the SU-35 fighter from the Mig-29

Answer 1

To find the total time for the missile to hit the enemy fighter if it is launched from the airfield, we can use the formula:

time = distance / speed

First, we need to find the distance between the airfield and the enemy fighter. We can use the Pythagorean theorem to do this:

distance = sqrt((60-0)^2 + (30-15)^2 + (5-1)^2) = sqrt(3600 + 225 + 16) = sqrt(3841) = 62.01 km

Next, we need to find the speed of the missile. We can use the formula:

speed = relative velocity + own velocity

To find the relative velocity of the enemy fighter with respect to the missile, we can use the formula:

relative velocity = speed of enemy fighter - speed of missile

Plugging in the given values, we get:

relative velocity = 1.7 - 3.5 = -1.8 mach

Adding the relative velocity to the speed of the missile, we get:

speed = -1.8 + 3.5 = 1.7 mach

Plugging the distance and speed into the time formula, we get:

time = 62.01 / 1.7 = 36.47 seconds

To find the distance traveled by the enemy's air-to-air missile if the base was not alerted by the radar and the enemy launches the missile at the SU-35, we can use the same formula:

time = distance / speed

First, we need to find the distance between the enemy fighter and the SU-35. We are given that the enemy fighter is 7 km away from the SU-35, so the distance is 7 km.

Next, we need to find the speed of the missile. Plugging in the given values, we get:

speed = 2.7 mach

Plugging the distance and speed into the time formula, we get:

time = 7 / 2.7 = 2.59 seconds

To find the relative velocity of the SU-35 with respect to the enemy Mig-29, we can use the formula:

relative velocity = speed of SU-35 - speed of Mig-29

Plugging in the given values, we get:

relative velocity = 1.3 - 1.7 = -0.4 mach

This means that the SU-35 is moving 0.4 mach slower than the Mig-29 with respect to the Mig-29.