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 165.0  m and at a speed of 2.10  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 5.30  m/s2 in a direction 69.0  degrees below horizontally Southward for a time of 1.250 seconds.

At the end of the 7.5-s interval, the hawk misses the finch and has to "put on the brakes". He does so by controlling the contact forces on him by the air so as to produce an acceleration of 4.651  m/s2 in a direction 70.104  degrees above horizontally Northward for a time of 1.5 seconds.

1. What is the hawk's final velocity at the end of the 1.5-s interval?

2.

Once again, please assume that the hawk's acceleration during the 1.5-s interval is constant. What is the hawk's displacement during the 1.5-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.

You have now been tracking the hawk's motion for a total of 1.250 + 7.5 + 1.5 = 10.25 seconds.

3. What is the total Southward displacement of the hawk during those 10.25 seconds? Specify the direction with a plus or minus sign assuming that Southward is positive and Northward is negative.

4. Finally, what is the final altitude of the hawk at the end of those 10.25 seconds?

Answer 1