A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high (see Fig. 3-60). If the projectile lands on top of the cliff 6.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance. FIGURE 3-60 Problem 88. 88. Choose the origin to be the point from which the projectile is launched, and choose upward as the positive y direction. The y displacement of the projectile is 135 m, and the horizontal range of the projectile is 195 m. The acceleration in the y direction is a y = − g , and the time of flight is 6.6 s. The horizontal velocity is found from the horizontal motion at constant velocity. Δ x = v x t → v x = Δ x t = 195 m 6.6 s = 29.55 m/s Calculate the initial v velocity from the given data and Eq. 2-12b. y = y 0 + v y 0 t + 1 2 a y t 2 → 135 m = v y 0 ( 6.6 s ) + 1 2 ( − 9.80 m/s) 2 = 60 m/s → v y 0 = 52.79 m/s Thus the initial velocity and direction of the projectile are as follows. v 0 = v x 2 + v y 0 2 = ( 29.55 m/s) 2 + (52 .79 m/s) 2 = 60m/s θ = tan − 1 v y 0 v x = tan − 1 52.79 m/s 29.55 m/s = 61 °
A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high (see Fig. 3-60). If the projectile lands on top of the cliff 6.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance. FIGURE 3-60 Problem 88. 88. Choose the origin to be the point from which the projectile is launched, and choose upward as the positive y direction. The y displacement of the projectile is 135 m, and the horizontal range of the projectile is 195 m. The acceleration in the y direction is a y = − g , and the time of flight is 6.6 s. The horizontal velocity is found from the horizontal motion at constant velocity. Δ x = v x t → v x = Δ x t = 195 m 6.6 s = 29.55 m/s Calculate the initial v velocity from the given data and Eq. 2-12b. y = y 0 + v y 0 t + 1 2 a y t 2 → 135 m = v y 0 ( 6.6 s ) + 1 2 ( − 9.80 m/s) 2 = 60 m/s → v y 0 = 52.79 m/s Thus the initial velocity and direction of the projectile are as follows. v 0 = v x 2 + v y 0 2 = ( 29.55 m/s) 2 + (52 .79 m/s) 2 = 60m/s θ = tan − 1 v y 0 v x = tan − 1 52.79 m/s 29.55 m/s = 61 °
A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high (see Fig. 3-60). If the projectile lands on top of the cliff 6.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.
FIGURE 3-60
Problem 88.
88. Choose the origin to be the point from which the projectile is launched, and choose upward as the positive y direction. The y displacement of the projectile is 135 m, and the horizontal range of the projectile is 195 m. The acceleration in the y direction is ay = −g, and the time of flight is 6.6 s.
The horizontal velocity is found from the horizontal motion at constant velocity.
Δ
x
=
v
x
t
→
v
x
=
Δ
x
t
=
195
m
6.6
s
=
29.55
m/s
Calculate the initial v velocity from the given data and Eq. 2-12b.
y
=
y
0
+
v
y
0
t
+
1
2
a
y
t
2
→
135
m
=
v
y
0
(
6.6
s
)
+
1
2
(
−
9.80
m/s)
2
= 60 m/s
→
v
y
0
=
52.79
m/s
Thus the initial velocity and direction of the projectile are as follows.
v
0
=
v
x
2
+
v
y
0
2
=
(
29.55
m/s)
2
+ (52
.79 m/s)
2
=
60m/s
θ
=
tan
−
1
v
y
0
v
x
=
tan
−
1
52.79
m/s
29.55
m/s
=
61
°
A shell is fired from a cliff that is 36 m above a horizontal plane. The muzzle speed of the shell is 80.0 m/s and it is fired at an elevation of 25° above the horizontal.
(a) Determine the horizontal range of the shell.(b) Determine the velocity of the shell as it strikes the ground.
In 2007, Michael Carter (U.S.) set a world record in the shot put with a throw of 24.77 m. What was
the initial speed of the shot if he released it at a height of 2.10 m and threw it at an angle of 38.0°
above the horizontal? (Although the maximum distance for a projectile on level ground is achieved
at 45° when air resistance is neglected, the actual angle to achieve maximum range is smaller; thus,
38° will give a longer range than 45° in the shot put.)
A projectile is fired with an initial speed of 40 m/s at angle of 23 degrees above the horizontal on a long flat firing range. Determine (1) the maximum vertical distance reached by the projectile, (2) the total time in the air, (3) the range of the projectile, (4) the velocity of the projectile 2 s after firing.
Chapter 3 Solutions
Physics for Scientists and Engineers with Modern Physics
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