A hawk is flying horizontally Southward at an altitude of 17

A hawk is flying horizontally Southward at an altitude of 177.0  m and at a speed of 2.20  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 4.90  m/s2 in a direction 70.0  degrees below horizontally Southward for a time of 0.950 seconds.

Part A

What is the hawk\'s final velocity at the end of the 0.950-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.

Part B

What is the hawk\'s displacement during the 0.950-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.

Part C

What is the hawk\'s displacement during the 8.5-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.

At the end of the 8.5-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 5.246  m/s2 in a direction 72.334  degrees above horizontally Northward for a time of 0.7 seconds.

Part D

What is the hawk\'s final velocity at the end of the 0.7-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. If the direction is above horizontally South instead of below, use a negative angle.

Part E

Once again, please assume that the hawk\'s acceleration during the 0.7-s interval is constant. What is the magnitude of the hawk\'s displacement during the 0.7-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.

Part F

What is the total Southward displacement of the hawk during those 10.15 seconds? Specify the direction with a plus or minus sign assuming that Southward is positive and Northward is negative.

Solution

Part a

We know that w

w = w₀ + alpha*t

w₀ = 2.20 m/s

alpha = 4.90 m/s2

t = 0.95 s

w = 2.20+ 4.9*0.95 = 6 m/s

but alpha is in the direction of 70 deg

so we will take its sin

4.9*sin70 = 4.6044 m/s2

hence w = 2.20 + 4.6044*0.95 = 6.574 m/s towards south

and cos component will take it eastward

w = 0 + 4.9*cos70*0.95 =1.592 m/s

hence resultant speed = sqrt(6.574² + 1.592²) =6.764 m/s

direction = tan^-1(1.592/6.574) = 13.613 deg