Complete the following problems to gain problem solving experience: 1. A missile

Question

Complete the following problems to gain problem solving experience: 1. A missile base is on alert at the origin (Point B) of the Cartesian axis in the figure below when it sees an enemy tank traveling due East at a constant velocity of magnitude 3.0 m/s and a distance 20 m away (Point A). A missile is fired from the origin with 0 initial speed and a constant acceleration of magnitude 0.40 m/s^2 at the instant that the tank passes the y - axis. What angle theta between the acceleration vector and the positive y - axis would result in a direct hit? 2. To sink an enemy ship 1km away, a battleship fires a projectile at an angle of 20 degrees. The crew then notices another ship 1.5km away. What new angle should they use to hit this ship with a projectile? You may assume the initial and final heights of the projectile are equal to zero.

Explanation / Answer

The x component of the enemy tank is given by

xtank = (3.0 m/s)t
ytank = 20 m

Now, for the missle,

xmissile = 1/2 (0.40 sin theta) t^2
ymissile = 1/2 (0.40 cos theta) t^2

Setting the x and y coordinates equal,

1/2 (0.40 sin theta) t^2 = 3.0t

1/2 (0.40 cos theta) t^2 = 20

Hence,

(sin theta) t = 15.0

(cos theta) t^2 = 100

Squaring the first equation,

(sin^2 theta)t^2 = 225

(cos^2 theta) t^2 = 100

Adding these, sin^2 theta + cos^2 theta = 1,

t^2 = 325

t = 18.027

Thus, as

(sin theta) t = 15.0

(sin theta) (18.027) = 15.0

sin theta = 0.83205

theta = 56.31 degrees [ANSWER]

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