Problems 35–37 investigate the motion of a projectile shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9 . 8 m∕sec 2 , and the muzzle velocity, υ 0 = 500 m∕sec, at which the projectile leaves the cannon. The angle θ , in degrees, between the muzzle of the cannon and the ground can vary. The time that the projectile stays in the air is r ( θ ) = 2 υ 0 g sin π θ 180 = 102 sin π θ 180 seconds . (a) Find the time in the air for θ = 20°. (b) Find a linear function of θ that approximates the time in the air for angles near 20°. (c) Find the time in air and its approximation from part (b) for 21°
Problems 35–37 investigate the motion of a projectile shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9 . 8 m∕sec 2 , and the muzzle velocity, υ 0 = 500 m∕sec, at which the projectile leaves the cannon. The angle θ , in degrees, between the muzzle of the cannon and the ground can vary. The time that the projectile stays in the air is r ( θ ) = 2 υ 0 g sin π θ 180 = 102 sin π θ 180 seconds . (a) Find the time in the air for θ = 20°. (b) Find a linear function of θ that approximates the time in the air for angles near 20°. (c) Find the time in air and its approximation from part (b) for 21°
Problems 35–37 investigate the motion of a projectile shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9.8 m∕sec2, and the muzzle velocity, υ0 = 500 m∕sec, at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary.
The time that the projectile stays in the air is
r
(
θ
)
=
2
υ
0
g
sin
π
θ
180
=
102
sin
π
θ
180
seconds
.
(a) Find the time in the air for θ = 20°.
(b) Find a linear function of θ that approximates the time in the air for angles near 20°.
(c) Find the time in air and its approximation from part (b) for 21°
If sec(a)
4964
250
88
88
13
find the value of cot(a) where a terminates in the first quadrant.
3.19 A cameraman is filming a marathon. He wants to keep his camera pointed at the
lead runner, but since he is not allowed to leave his current location he must rotate the
camera to keep the runner in frame. At the instant shown in Figure 3.23, 0 = 50°, the
runner has a speed of 6.00 m/s and an acceleration of 0.10 m/s² to the left. What are
the values of and Ö at this instant?
camera
0,0
Vrunner
20m
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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