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 very tall light standard is swaying in an east-west direction in a strong wind. An observer notes that the time difference between the vertical position and the furthest point of sway was 2 seconds. The pole is 40 metres tall. At the furthest point of sway, the tip of the pole is 1° out of the vertical position when measured from the bottom of the pole. Create a sinusoidal equation that models the motion of the tip of the pole as a displacement from the vertical position as a sinusoidal function of time. Assume time starts when the tip of the pole is furthest east. Include a sketch of the graph of your equation. (4 marks)
An electron moves with a constant horizontal velocity of 3.0 x 100 m/s and no initial vertical velocity as it enters a deflector inside a TV tube. The electron strikes the screen after traveling
17.0 cm horizontally and 40.0 cm vertically upward with no horizontal acceleration. What is the constant vertical acceleration provided by the deflector? (The effects of gravity can be ignored.)
1.4 x 10 m/s?
14
2.5 x 10 m/s2
14
1.2 x 10 m/s?
8.3 x 10 m/s?
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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