a footballer kicks a ball vertically upwards. initially, the ball is stationary. his boot is in contact with the ball for 0.05s.
2 answers:
Answer:
The ball rises to a height of 20.4 meters.
Explanation:
Since we know the speed at which the ball starts rising, we can ignore the other data. The height reached by the ball can be obtained using the kinematics equation:
Since the velocity at the highest point is zero, we can solve for the height y at that point:
Plugging in the given value for the initial velocity, and assuming that the acceleration due to gravity g is 9.8m/s², we obtain:
It means that the ball rises to a height of 20.4 meters.
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Answer:
The rotational frequency must be 2073.56 rpm
Explanation:
Notice that we need to obtain a rotational frequency in "rpm" (revolutions per minute), so we better start by converting all the given information into the appropriate units:
The magnitude of the velocity for the pitch is given in miles per hour, while the diameter of the machine's wheels is given in cm. Let's reduce all units of length into meters(using the metric system), and the units of time into minutes.
Conversion of the 85 mph speed into meters per minute:
Recall that 1 mile equals 1609.34 meters, and that 1 hour equals 60 minutes, so we write:
which can be rounded to approximately 2280 m/min.
We also convert the 35 cm diameter into meters:
diameter = 0.35 m
Now we use the equation that relates angular velocity (w) and the radius (R) of the circular movement, with tangential velocity (), in order to obtain the angular velocity of the wheel:
but recall that this angular velocity is given in radians per unit of time. So first find the radius of the wheel (half its diameter). R = 0.175 m
So we have:
And now, recalling that radians equal one revolution, we convert the angular velocity ot revolutions per minute by dividing the "w" we found by
:
rotational frequency =
observer is standing at distance d = 60 m south from the intersection
cyclist is travelling at speed v = 10 m/s
now after t = 8 s its displacement from intersection is given by
so the position of cyclist makes an angle with the observer
now the component of velocity of cyclist along the line joining its position with the observer is given as
here
so at this instant cyclist is moving away with speed 8 m/s
Answer:
6.18 m/s
Explanation:
Roller skate collision
The final direction of the system (me=M + person=P) velocity vector is at an angle; Ф, to the direction running south to north. Apply the component form of the impulse-momentum equation, firstly;
x-axis component form (+x east);
+
+
=
+
Ф
60 ·8 + 0 = (60 + 80)Ф
480 = 140Ф................. (I)
y-axis component form (+y north);
+
+
=
+
Ф
0 + 80.9 = (60 + 80)Ф
720=
140Ф
140Vf=Ф......................................(2)
Substituting (2) into (1) to give the angle;
480 = 720tan Ф
Ф = arctan(0.67) =33.69°.......................(3)
Evaluating (1) with (3) gives the velocity magnitude
480 = 140Vfsin 33.69°
Vf=6.18 m/s
note 1:
This angle corresponds to a direction; 90° - 33.69° = 56.31° north of east.