Physics Problems

2008-08-24 7:05 pm

1. An airplane has an airspeed of 200km/h. The pilot wants to reach an airport 650 km due east but the wind is blowing 50km/h in the direction 30 degrees north of east. In what direction must the pilot head in order to reach the airport(assume he will travel in straightline)?

2. A computer hard disk starts from rest, then speeds up with augular acceleration of 190 rad/s^2 until it reaches a final velocity of 6500 rpm. How many revolutions has the disk made 10.0s after it starts?

3. A soccer player kicks a ball at an angle of 42 degrees to the horizontal. The ball leaves his foot with a velocity of 18m/s. The player that receives this ball is standing 46m from the kicker. How fast does the receiver need to receive the ball before it hits the ground?

Please answer with detailed steps and explainations. Thanks.

回答 (1)

keaneutd

2008-08-24 9:34 pm

✔ 最佳答案

Q1: You have to balance out the component of wind perpendicular to the route.
Let x be direction of plane heading (south of east)
50sin30 = 200sinx
x=7.18 (south of east)

Q2:
Final angular velocity = (6500*2*pi/60) rad/s
Time required to reach final ang vel = (6500*2*pi/60 - 0)/190 = 3.5825s
Angular displacement during acceleration
= 0.5 * a * t^2 = 0.5 * 190 * 3.5825^2 = 1219.2713 rad
Angular displacement during constant angular velocity
= (6500*2*pi/60) * (10-3.5825) = 4368.2415 rad
Total revolution = (1219.2713 4368.2415) / (2 * pi) = 889.2803 revolutions

Q3: (Take upward direction as positive, assume no air resistancea)
Time for ball to reach ground:
Using s = ut 0.5a(t^2) [we consider vertical motion here]
0 = 18sin42 * t 0.5 * (-10) * (t^2)
t = 2.4089s

Horizaontal distance travelled by ball
= 18cos42 * 2.4089
= 32.2225m

Speed of receiver
= (46-32.2225)/2.4089
= 5.7195 m/s

2008-08-24 13:38:57 補充：
I don't know why every time I have all "+" removed...
So for Q2:
Total revolution = (1219.2713 + 4368.2415) / (2 * pi) = 889.2803 revolutions

And beginning of Q3:

Using s = ut + 0.5a(t^2) [we consider vertical motion here]
0 = 18sin42 * t + 0.5 * (-10) * (t^2)
t = 2.4089s

參考: Myself

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