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Converted document DYNAMICS PROBLEMS

DYNAMICS PROBLEMS

Example: Helicopter launching an ordinance

Consider that a helicopter is used to launch an ordinance with a speed of U_launch = 50 km/h along the body of the helicopter.

Figure 1 Figure of a helicopter bomber.

What would be the range of the bomb that is launched by such a helicopter that is flying at an altitude H of 500 m? Assume that the helicopter is in hover (U_cruise = 0).
Assume that this bombing helicopter is performing a maneuver in which it has to climb at a velocity of U_climb = 200 km/h at an angle of 45 degrees to launch a bomb. What is the maximum range of the bomb with respect to the ground?

Figure 2 Trajectory of the bomb which has been launched by the helicopter in hover U_cruise = 0 with an initial forward velocity U_launch = 50 km/h.

Assume that acceleration due to gravity is 9.8 m/s.

Solution

Figure 3 Free body diagram of the bomb after it has been launched.

The motion of the bomb is a projectile motion such that it has an initial velocity of 50 km/h in the horizontal direction (x-axis). Thus u_initial = U_launch = 50 km/h.
After the bomb is launched, there are is no external force acting along the x-axis. Thus:

F_x = ma_x = 0

⇒ a_x = 0

Since a_x = (du)/(dt), it implies that the bomb has a constant velocity along the x-axis. Similarly, distance traveled in the x-axis is given by:

^R⌠⌡₀dx = ^t⌠⌡₀udt

which gives,

(1) R = ut