PHY 105   Test 2    May 23, 2002      30 minutes

La Salle University

Dr. R. A. DiDio

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1.   [15 pts] A helicopter is flying horizontally at 60.0 m/s when a front wheel falls off.  The altitude of the helicopter is 300 m when this occurs.

a)      How much time is required for the tire to hit the earth?

 

Solution:  This is a projectile problem with an initial height above the ground (300 m), and only a horizontal velocity (60 m/s).  Therefore, t­Air can be calculated from:  .  Solving for t yields tAir:       

 

 

 

b)      How far does it travel horizontally while falling?

 

Solution:  Given the air time and the initial horizontal velocity, the range is determined by  .

 

 

c)      Find the horizontal and vertical components of velocity when it hits the ground.

 

Solution:  The x-component of velocity is still 60 m/s.  The y-component of velocity is determined by since there is no initial velocity in the y-direction.  When the tire hits the ground and therefore

 

 

 

2.   [10 pts] A subway train starts from rest and accelerates at a rate of 1.60 m/s2 for 14.0 s.  It runs at constant speed for 70.0 s and slows down at a rate of 3.50 m/s2 until it stops at the next station. What is the total distance covered?

 

Solution:  There are three legs on this trip –

 

Leg I – Constant acceleration of 1.6m/s2  for 14 s:  

 

Leg 2 – Constant velocity for 70 seconds.  The velocity is the velocity after the initial 14 second acceleration:

.  Therefore, the distance traveled in Leg 2 is (22.4 m/s) (70 s) = 1568 m.

 

Leg 3 – Negative acceleration of –3.5 m/s2 from 22.4 m/s to 0 m/s.  Since you know beginning and ending velocities, find the distance traveled using .  Therefore

 and distance traveled = 71.68 m

 

Total Distance Traveled = 156.8 + 1568 + 71.68 m = 1.80 x 103 m

 

 

 

3.   [10 pts] A particle is at position (-1 m, 2 m) in the x-y plane, moving with velocity  .  It experiences constant acceleration of  for 3 seconds

 

a)      Where is the particle after 3 seconds? (Express your answer as a position vector)

 

Solution:  Use the vector form of the motion with constant acceleration: (Note – all position, velocity, and acceleration are in appropriate SI units)

 

In this problem . Therefore

 

At t = 3 s,

 

 

 

 

 

 

 

b)      What is the average velocity of the particle in the first 3 seconds?

Solution:  Use the vector definition of average velocity

 where

                                                                                                        

Using the initial positon and the position from (a) as r1 and r2, respectively,