Ship A is about to launch a mortar shell at Ship B. The Kinematics of this probl

Question

Ship A is about to launch a mortar shell at Ship B.  The Kinematics of this problem actually allows for two different launch angles that can be used to strike Ship B.

SOLVE for these TWO different angles.

Given information:

Ship A and Ship B are stationary.

The separation distance between the ships is 500m

The magnitude of the initial velocity vector for the mortar shell is 100 m/s     (regardless of the launch angle)

show all work

a. Derive an expression for the launch angle.   (Hint: the launch angle is independent of time)

b.  Solve for the two different launch angles using the given information.                                                                

Ship A is about to launch a mortar shell at Ship B. The Kinematics of this problem actually allows for two different launch angles that can be used to strike Ship B. SOLVE for these TWO different angles. Given information: Ship A and Ship B are stationary. The separation distance between the ships is 500m The magnitude of the initial velocity vector for the mortar shell is 100 m/s (regardless of the launch angle) show all work Derive an expression for the launch angle. Solve for the two different launch angles using the given information.

Explanation / Answer

Horizontal motion:

time = distance/v*cosx    x: angle of projection (launch)

Vertical motion:

time = 2*v*sinx/g     g: gravity

thus, distance/(v*cosx) = 2*v*sinx/g

v^2 * sin2x = distance*g

sin2x = (distance*g)/v^2; derivation for launch angle x

sin2x = 500*10/(100*100) = 0.50

2x = 30 or 2x = 150

x = 15 or x = 75

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