Physics problems: kinematics

Part 3


Problem 21.

An aircraft has a lift-off of 120km/h.

(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240m?

(b) How long does it take the aircraft to become airborne?



Problem 22.

A ball is thrown vertically upward with a speed of 25.0m/s.

(a) How high does it rise?

(b) How long does it take to reach its highest point?

(c) How long does the ball take to hit the ground after it reaches its highest point?

(d) What is its velocity when it returns to the level from which it started?



Problem 23.

A tortoise and a hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000 meters at a speed of 0.2 m/s. The rabbit runs the first 200 meters at 2 m/s, stops to take a nap for 1.3 hours, and awakens to finish the last 800 meters with an average speed of 3 m/s. Who wins the race and by how much time?



Problem 24.

The slowest animal ever discovered is a crab found in the Red Sea that travels an average speed of 5.7 km/year. How long will it take this crab to travel 1 meter?



Problem 25.

A "moving sidewalk" in a busy airport terminal moves 1 m/s and is 200 m long. A passenger steps onto one end and walks, in the same direction as the sidewalk is moving, at a rate of 2.0 m/s relative to the moving sidewalk. How much time does it take the passenger to reach the opposite end of the walkway?





Problem 26.

Assume it takes 8 minutes to fill a 35.0 gal gasoline tank. (1 U.S. gal = 231 cubic inches)
(a) Calculate the rate at which the tank is filled in gallons per second.
(b) Calculate the rate at which the tank is filled in cubic meters per second.
(c) Determine the time interval, in hours, required to fill a volume at the same rate.



Problem 27.

A plane flies 955 km due east, then turns due north and flies another 469 km. Draw an x-y axis at the starting point with the positive x-axis pointing east, and determine the polar coordinates of the plane's finale position.



Problem 28.

A car travels east at 89 km/h for 1 h. It then travels 26 east of north at 141 km/h for 1 h.

(a) What is the average speed for the trip?

(b) What is the average velocity for the trip?



Problem 29.

(a) If a particle's position is given by   (where t is in seconds, and x is in meters), what is it's velocity at t=1s? 

(b) what is it's speed at t=1s? 

(c) Is there ever an instant when the velocity is 0?  If so, give the time.



Problem 30.

The captain of a plane wishes to proceed due west. The cruising speed of the plane is 245 m/s relative to the air. A weather report indicates that a 38-m/s wind is blowing from the south to the north. In what direction, measured to due west, should the pilot head the plane relative to the air?




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