Physics Chapter 4
Problems (Chapter 3)
Review Example problems #1 - 12 by yourself.
Problem 3 (page 96): A web page designer creates an animation in which a dot on a computer screen has a position of r = [4 cm + (2.5 cm/s2)t2]i + (5 cm/s)t j. a) Find the magnitude and direction of the dot’s average velocity between t = 0 and t = 2 s. b) Find the magnitude and direction of the instantaneous velocity at t = 0, t = 1 s, nd t = 2 s. c) Sketch the dot’s trajectory from t = 0 to t = 2 s, and show the velocities calculated in part (b).
(a) Identify and Set Up: From [pic] we can calculate x and y for any t. Then use Eq. (3.2), in component form. Execute: [pic] At [pic] [pic] At [pic] [pic] [pic] [pic]
| |[pic] …show more content…
The acceleration at this point in the motion is [pic] downward. (c) Set Up: The time to make one rotation is the period T, and the speed v is the distance for one revolution divided by T. Execute: [pic] so [pic] Evaluate: The radial acceleration is constant in magnitude since v is constant and is at every point in the motion directed toward the center of the circular path. The acceleration is perpendicular to [pic] and is nonzero because the direction of [pic] changes.
Problem 63 (page 100): A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.63. Use information from the Figure to find:
(a) The initial speed of the grasshopper
(b) The height of the cliff. [pic]
Identify: From the figure in the text, we can read off the maximum height and maximum horizontal distance reached by the grasshopper. Knowing its acceleration is g downward, we can find its initial speed and the height of the cliff (the target
Review Example problems #1 - 12 by yourself.
Problem 3 (page 96): A web page designer creates an animation in which a dot on a computer screen has a position of r = [4 cm + (2.5 cm/s2)t2]i + (5 cm/s)t j. a) Find the magnitude and direction of the dot’s average velocity between t = 0 and t = 2 s. b) Find the magnitude and direction of the instantaneous velocity at t = 0, t = 1 s, nd t = 2 s. c) Sketch the dot’s trajectory from t = 0 to t = 2 s, and show the velocities calculated in part (b).
(a) Identify and Set Up: From [pic] we can calculate x and y for any t. Then use Eq. (3.2), in component form. Execute: [pic] At [pic] [pic] At [pic] [pic] [pic] [pic]
| |[pic] …show more content…
The acceleration at this point in the motion is [pic] downward. (c) Set Up: The time to make one rotation is the period T, and the speed v is the distance for one revolution divided by T. Execute: [pic] so [pic] Evaluate: The radial acceleration is constant in magnitude since v is constant and is at every point in the motion directed toward the center of the circular path. The acceleration is perpendicular to [pic] and is nonzero because the direction of [pic] changes.
Problem 63 (page 100): A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.63. Use information from the Figure to find:
(a) The initial speed of the grasshopper
(b) The height of the cliff. [pic]
Identify: From the figure in the text, we can read off the maximum height and maximum horizontal distance reached by the grasshopper. Knowing its acceleration is g downward, we can find its initial speed and the height of the cliff (the target