As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of 132 ft / s and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of 7.5 ft / s 2 . (a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes. (b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.
As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of 132 ft / s and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of 7.5 ft / s 2 . (a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes. (b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.
As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of
132
ft
/
s
and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of
7.5
ft
/
s
2
.
(a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes.
(b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
The minute hand of a wall clock measures 24 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the magnitude and angle from a quarter after the hour to half past, the magnitude and angle for the next half hour, and the magnitude and angle for the hour after that? (Use a coordinate system with the origin at the clock center, +x rightward toward the "3:00" position, and +y upward toward the "12:00" position.)
(a) the magnitude from a quarter after the hour to half past cm(b) the angle from a quarter after the hour to half past ° (counterclockwise from the +x-axis)(c) the magnitude for the next half hour cm(d) the angle for the half hour in part (c) ° (counterclockwise from the +x-axis)(e) the magnitude for the hour after that cm(f) What is the angle for the hour in part (e) ° (counterclockwise from the +x-axis)
How much force must be applied to a 1.8kg ice hockey puck to give it an acceleration of 10 m s-2
A cannon is fired at an angle of 75° with the ground at an initial velocity of 250 m/s. Calculate the speed of
the cannon three seconds after its launch.
Chapter 12 Solutions
Calculus Early Transcendentals, Binder Ready Version
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.