A pilot flies with a heading of 160° and an airspeed of 250 km/h. There is a steady wind of 30 km/h from the direction of 030°. Calculate the ground velocity of the plane.

Questions 1 through 3 pertain to the situation described below: An archer wants to launch an arrow from a bow to clear a treetop that is 35.0 m vertically above, and 97.0 m horizontally away from, the launching location. Assume that the launching speed is 57.0 m/s and the launching angle is 0 above the horizontal. (1) How much does the arrow clear the treetop if 0 = 30.0°? (A) 3.6 m; (B) 3.1 m; (C) 2.6 m; (D) 2.1 m; (E) 1.6 m. (2) What is the maximum horizontal range of the arrow if 0 can vary? (A) 212 m; (B) 242 m; (C) 272 m; (D) 302 m; (E) 332 m. (3) What is the range of 0 for the arrow to clear the treetop? (A) 29.9-86.0°; (B) 28.9–81.0°; (C) 27.9–76.0°; (D) 26.9–71.0°; (E) 25.9–66.0°.

A train at a constant 48.0 km/h moves east for 26.0 min, then in a direction 50.0° east of due north for 21.0 min, and then west for 36.0 min. What are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip?

44. A metal ramp 6.00 m long is tilted 10.0° and is used to load and unload a moving van. Suppose a 20.0 kg box is pushed up the ramp and it slides with a friction coefficient of 0.30. The ramp can be viewed as a “machine” where the useful output is the potential energy gain of the box and the input is the physical work done by the person doing the pushing. (a) Determine the efficiency of the ramp. (b) Determine the ratio of the force needed to lift the box without the ramp to the force needed to push it along the ramp (this is called the mechanical advantage).

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.50 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = −       yi =     (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x =          y =   (f) How long does it take the ball to reach a point 10.0 m below the level of launching?

Initially, a particle is moving at 5.45 m/s at an angle of 38.5 above the horizontal. Four seconds later, its velocity is 6.24 m/s at an angle of 54.3 below the horizontal. What was the particle's average acceleration during these 4.00 seconds in the x-direction (enter first) and the y-direction?

A train at a constant 61.0 km/h moves east for 38.0 min, then in a direction 55.0° east of due north for 29.0 min, and then west for 48.0 min. What are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip?

A projectile's launch speed is 6.30 times its speed at maximum height. Find the launch angle θ0.

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.80 m/s and angle of 16.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi =       yi =

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 9.00 m/s and angle of 21.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi =       yi =       (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x =  m/s vi, y =  m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x =        m y =        m (d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How…