(II) Here is something to try at a sporting event. Show that the maximum height h attained by an object projected into the air, such as a baseball, football, or soccer ball, is approximately given by h ≈ 1.2 t 2 m , where t is the total time of flight for the object in seconds. Assume that the object returns to the same level as that from which it was launched, as in Fig. 3–42. For example, if you count to find that a baseball was in the air for t = 5.0 s, the maximum height attained was h = 1.2 × (5.0) 2 = 30 m. The beauty of this relation is that h can be determined without knowledge of the launch speed υ 0 or launch angle θ 0 . FIGURE 3–42 Problem 42.
(II) Here is something to try at a sporting event. Show that the maximum height h attained by an object projected into the air, such as a baseball, football, or soccer ball, is approximately given by h ≈ 1.2 t 2 m , where t is the total time of flight for the object in seconds. Assume that the object returns to the same level as that from which it was launched, as in Fig. 3–42. For example, if you count to find that a baseball was in the air for t = 5.0 s, the maximum height attained was h = 1.2 × (5.0) 2 = 30 m. The beauty of this relation is that h can be determined without knowledge of the launch speed υ 0 or launch angle θ 0 . FIGURE 3–42 Problem 42.
(II) Here is something to try at a sporting event. Show that the maximum height h attained by an object projected into the air, such as a baseball, football, or soccer ball, is approximately given by
h
≈
1.2
t
2
m
,
where t is the total time of flight for the object in seconds. Assume that the object returns to the same level as that from which it was launched, as in Fig. 3–42. For example, if you count to find that a baseball was in the air for t = 5.0 s, the maximum height attained was h = 1.2 × (5.0)2 = 30 m. The beauty of this relation is that h can be determined without knowledge of the launch speed
υ
0
or launch angle
θ
0
.
(i)
Height: A ball is kicked up from the ground with an initial velocity of 48 meter per second. The
height of the ball from the ground is given by the formula
h = -16r + 481, where r is the time in seconds. Find the maximum height reached by the ball.
Gi)
World Population: The function given by the formula f(x)- 0.000478x- 1.813x + 1720.1 models
world population in billions from 1950 to 2025.
a) Evaluate f(1985) and interpret the result.
b) Estimate the world population today.
c) According to tis model, when did the world population reach 7 billion?
d) Discuss the implication presented by the difference in your answers in part a and b.
(II) A stone is thrown vertically upward with a speed of 24.0 m/s(a) How fast is it moving when it is at a height of 13.0 m? (b) How much time is required to reach this height? (c) Why are there two answers to (b)?
(II) Extreme-sports enthusiasts have been known to jump
off the top of El Capitan, a sheer granite cliff of height
910 m in Yosemite National Park. Assume a jumper runs
horizontally off the top of El Capitan with speed 4.0 m/s
and enjoys a free fall until she is 150 m above the valley
floor, at which time she opens her parachute (Fig. 3–37).
(a) How long is the jumper in free fall? Ignore air resis-
tance. (b) It is important to be as far away from the cliff
as possible before opening the parachute. How far from
the cliff is this jumper when she opens her chute?
4.0 m/s
910 m
150 m
FIGURE 3-37
Problem 26.
Chapter 3 Solutions
Physics for Scientists and Engineers with Modern Physics
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.