A soccer player kicks a ball with an initial speed to 14 m/s at an angle θ with the horizontal (see the accompanying figure). The ball lands 18 m down the field. If air resistance is neglected, then the ball will have a parabolic trajectory and the horizontal range R will be given by R = υ 2 g sin 2 θ where v is the initial speed of the ball and g is the acceleration due to gravity. Using g = 9.8 m/s 2 , approximate two values of θ , to the nearest degree, at which the ball could have been kicked. Which angle results in the shorter time of flight? Why?
A soccer player kicks a ball with an initial speed to 14 m/s at an angle θ with the horizontal (see the accompanying figure). The ball lands 18 m down the field. If air resistance is neglected, then the ball will have a parabolic trajectory and the horizontal range R will be given by R = υ 2 g sin 2 θ where v is the initial speed of the ball and g is the acceleration due to gravity. Using g = 9.8 m/s 2 , approximate two values of θ , to the nearest degree, at which the ball could have been kicked. Which angle results in the shorter time of flight? Why?
A soccer player kicks a ball with an initial speed to
14
m/s
at an angle
θ
with the horizontal (see the accompanying figure). The ball lands
18
m
down the field. If air resistance is neglected, then the ball will have a parabolic trajectory and the horizontal range
R
will be given by
R
=
υ
2
g
sin
2
θ
where
v
is the initial speed of the ball and
g
is the acceleration due to gravity. Using
g
=
9.8
m/s
2
, approximate two values of
θ
,to the nearest degree, at which the ball could have been kicked. Which angle results in the shorter time of flight? Why?
A projectile is given an initial velocity of 31.5 m/s at an angle of 51.5 degrees with respect to the horizontal. How far has it moved in the x-direction at the time when its speed in the y-direction is 10.5 m/s?
A projectile is launched with an initial velocity of 27.2 m/s at 64.7 degrees with respect to the horizontal. What is the speed of the projectile 1.83 s after being launched. Assume the speed is measured in m/s.
A projectile is launched with an initial velocity of 46.8 m/s at an angle of 31.2 degrees with respect to the horizontal. In meters, what is the maximum upward displacement of the projectile?
A tracking radar lies in the vertical plane of the path of a rocket which is coasting in unpowered flight above the atmosphere (Figure Q7). For the instant when ? = 30°, the tracking data give r = 25(104) ft, ?̇ = 4000 ft /sec, and ?̇ = 0.80 deg/sec. The acceleration of the rocket is due only to gravitational attraction and for its particular altitude is 31.4 ft/???2 vertically down. For these conditions determine the velocity v of the rocket.
Alex is measuring the time-averaged velocity components in a pump using a laser Doppler velocimeter (LDV). Since the laser beams are aligned with the radial and tangential directions of the pump, he measures the ur and u? com ponents of velocity. At r = 5.20 in and ? = 30.0°, ur = 2.06 ft/s and u? = 4.66 ft/s. Unfortunately, the data analysis program requires input in Cartesian coordinates (x, y) in feet and (u, ?) in ft/s. Help Alex transform his data into Cartesian coordinates. Specifically, calculate x, y, u, and ? at the given data point.
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