Birds have evolved to the ability to control their motions through the air by co

Question

Birds have evolved to the ability to control their motions through the air by controlling the forces exerted on their bodies by the air; the contact forces on a bird by the air plus the force of gravity on the bird by the Earth determine the change in motion of the bird at any instant of time. In this problem, you will be asked to use what you know about acceleration to track the motion of a diving hawk.

A hawk is flying horizontally Southward at an altitude of 132.0  m and at a speed of 2.40  m/s when he spots a slow-flying finch ahead of his current location and below his current path. At time zero, the hawk starts a dive by controlling the contact forces on him by the air so as to produce an acceleration of 5.10  m/s2 in a direction 68.0  degrees below horizontally Southward for a time of 0.750 seconds.

Part C What is the hawk's displacement during the 7.5-s interval? Give your answer as an ordered pair, with magnitude first, followed by a comma, then followed by the direction. Give the direction in terms of an angle measured below the horizontally Southward direction. magnitude, direction m, degrees below South Submit XIncorrect; Try Again; 5 attempts remaining

Explanation / Answer

Hawk's speed is 24m/s southward, and acceleration is 5.10 m/s^2 in a direction 68.0 degrees below horizontally Southward. So, the component of the acceleration southwards is 5.1cos68= 1.91m/s^2 and vertically below is 5.1sin68= 4.73m/s^2.

Now, using the equation for motion;

Along southwards, distance travelled in 7.5s is x= speed*time + 0.5*acceleration*time^2 = 2.4*7.5 + 0.5*1.91*7.5^2= 71.72m

Similarly, along downwards, distance travelled in 7.5s is y= 0.5*4.73*7.5^2= 133m

Now, Hawk's displacement during the 7.5s interval is (x^2+y^2)^1/2= (71.72^2+133^2)^1/2 = 151.13m

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