(11%) Problem 1: A small plane flies a distance d1 = 46 km in a direction θ1 = 58o north of east and then flies d2 = 21 km in a direction θ2 = 15o north of east.
50% Part (a) What is the magnitude of the net displacement vector of the plane, in units of km?
dnet =
θnet =
(11%) Problem 2: A helicopter takes off over level ground, first rising vertically to a height of 170 m, then flying a straight-line distance of 257 m at an angle of 44.9 degrees above horizontal.
50% Part (a) What is the height of the helicopter at the end of these two displacements (in meters)?
h =
d =
(11%) Problem 3: After being marooned by his crew on an island in the Caribbean, Captain William Kidd builds a raft to escape and set out to sea on it. The wind seems quite steady, at first blowing him due east for 12 km and then 5 km in a direction 10 degrees north of east. Certain that he will eventually reach safety, he falls asleep. When he wakes up, he notices the wind is now blowing him gently 14 degrees south of east, and after traveling for 21 km in that direction, he finds himself back on the island!
50% Part (a) How far, as the crow flies, in kilometers, did the wind blow him while he was sleeping?
r =
θ =
(11%) Problem 4: An ice hockey player is moving at 8.00 m/s when he hits the puck toward the goal. The speed of the puck relative to the player is 29.0 m/s. The line between the center of the goal and the player makes a 90.0° angle relative to his path as shown in the figure.
θ =
(11%) Problem 5: In a time of 3.47 h, a bird flies a distance of 75.8 km in a direction 39.5 degrees east of north. Take north to be the positive y direction and east to be the positive x direction. Express your answers in km/h.
50% Part (a) What is the x component of the bird’s average velocity?
x =
50% Part (b) What is the y component of the bird’s average velocity?
y =
(11%) Problem 6: An airplane flies horizontally at a speed of 344 km/h and drops a crate that falls to the horizontal ground below. Neglect air resistance.
x =
50% Part (b) What was the speed of the crate, in m/s, just before it hit the ground?
v =
(11%) Problem 7: A quarterback throws a football with an initial velocity v at an angle θ above the horizontal. Assume the ball leaves the quarterback’s hand at ground level and moves without air resistance. All portions of this problem will produce algebraic expressions in terms of v, θ, and g. Let the origin of the Cartesian coordinate system be the ball’s initial position.
v0,y =
v0,x =
33% Part (c) Write an expression for the total time, ttotal, the football is in the air.
Ttotal =
(11%) Problem 8: A soccer ball is kicked from ground level across a level soccer field with initial velocity vector v0 = 12 m/s at θ = 31° above horizontal. The soccer ball feels wind resistance which causes it to slow horizontally with constant acceleration magnitude ax = 0.88 m/s2, while leaving its vertical motion unchanged. Assume any other air resistance is negligible. Choose the positive direction of x from initial point towards final point of flight. Use a Cartesian coordinate system with the origin at the ball’s initial position.
tf =
xmax =
(11%) Problem 9: A basketball shooting guard launches a free-throw with initial velocity v0 = 7.5 m/s at an angle θ = 29° above the horizontal. Use a Cartesian coordinate system with the origin located at the position the ball was released, with the ball’s horizontal velocity in the positive x direction and vertical component in the positive y-direction. Assume the basketball encounters no air resistance.
hmax =
t =
