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.
Chapter 5.9, Problem 96E
(a)
To determine
To calculate: The velocity of the object as a function of time when an object is dropped from a height 400 feet.
(b)
To determine
To calculate: The position of the object as a function of time when an object is dropped from a height 400 feet.
(c)
To determine
To prove: The velocity of the object as a function of time, v(t)=−32/ktanh(32kt) when an object is dropped from a height 400 feet.
(d)
To determine
To calculate: The limit of velocity that is limt→∞v(t) and its interpretation.
(e)
To determine
To calculate: The position s of the object as a function of time. Also, draw the graph of the position vector in parts (b) and (c) when k=0. The additional time required for the object to reach ground level when air resistance is not neglected.
(f)
To determine
The description when the value of k increases. Then test ascertain at a particular value of k.
A raindrop falls with acceleration 9.8
m/sec² , where "v" is its velocity. What is the
raindrop's velocity?
29.4(1 – e3) m/sec
29.4(e- 1) m/sec
29.4(1 – e5) m/sec
32.2 (e- 1) m/sec
A projectile is fired straight up from a platform 10ft above the ground, with an
initial velocity of 160 ft/sec. Assume that the only force affecting the motion of
the projectile during its flight is from gravity, which produces a downward
acceleration of 32 ft/sec?. What is the equation for the height of the projectile
above the ground as a function of time t if t = 0 when the projectile is fired?
s = -16t2 + 80t + 10
s = 16t2 – 160t + 10
-
O D
A
s = -16t2 – 160t + 10
s = -16t2 + 160t + 10
B
The period T of a pendulum of length L is T = (2 √L)/√g, where g is the acceleration due to gravity. A pendulum is moved from the Canal Zone, where g = 32.09 feet per second per second, to Greenland, where g = 32.23 feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.5 feet to 2.48 feet. Approximate the change in the period of the pendulum
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