Questions about Chapter 4: Motion in two and three dimension.

Q1. At t = 0 , a particle moving in the x-y plane with constant acceleration  a = ( i - 5 j ) m/s2, has vo = ( 3 i +5 j ) m/s at the origin.  Find the average velocity of this particle  between t = 0 and t = 4 s.

ANS:    ( 5 i  -  5 j )  m/s.

Q2. A car is traveling east with a speed of 36 m/s  and  a truck is traveling north with a speed of 28 m/s.  Find the velocity ( in unit vector notation ) of the car relative to the   truck.  What is the magnitude of this velocity ?

ANS:    ( 36 i - 28j ) m/s  ;  45.6 m/s.

Q3.   A river flows due north with a speed of 2.5 m/s. A man rows a boat to cross the  river, his speed relative to the water being 3.0 m/s.  In what direction should he  head the rowboat in order to reach a point on the opposite bank directly east from the start ?

ANS:    56.4o south of east.

Q4.  An aero plane flies north at a speed of 100 m/s in a wind blowing at 25 m/s toward the east.  What is the speed and direction in which the plane travels as seen by an  observer on the ground ?

ANS:    103 m/s  ,  14o east of north.

Q5.  A football is kicked off with an initial speed of 19.5 m/s at an angle of 45o to the  horizontal.  A receiver on the goal line 50 m away in the direction of the kick starts running to meet the ball at that instant.  What must be his minimum speed if he is to catch the ball just before it hits the ground ?

ANS:    3.98 m/s.

Q6.  A ball is kicked at an angle of 60o above the horizontal.  It hits a building 20 m away at a point 10 m above the ground.  Find the initial speed of the ball.

ANS:    17.8 m/s.

Q7.  The speed of a particle moving in a circle slows down at a rate of 2 m/s2.  At some instant, the magnitude of the total acceleration is 3 m/s2 and the particle speed is   12 m/s.  What is the radius of the circle ?

ANS:    64.4 m.

Q8. The moon’s nearly circular orbit about the earth has a radius of about 3.85x108 m and a period of 27.3 days.  Determine the acceleration of the moon toward the earth.

ANS:    2.73x10-3 s.

Q9.  At time t = 0 a particle leaves the origin with a velocity of 6 m/s in the +y direction.  Its acceleration is given by

a  =  ( 2 i - 3 j  )   m/s2.

When the particle reaches its maximum y co-ordinate, its y component of the          velocity is zero.  At this instant find its x and y co-ordinates.

ANS:    x   =   4 m ;      y    =    6 m.

Q10.     A ball is thrown up from the top of a building at an angle of 51o above the    horizontal. It strikes the ground 2.3 s later, at a horizontal distance of 17.5 m away          from the base of the building.

(a)  Find the initial speed of the ball.                           ANS: 12.1 m/s

(b)  Find the height of the building.                             ANS: 4.29 m

Q11.     The pilot of an airplane flies due north with a speed of 80 km/hr relative to the  ground.  There is a wind of 40 km/hr toward the east.  Taking the North direction along the positive y-axis and the East direction along the positive  x-axis.

(a) Find the velocity of the aircraft relative to the air in unit-vector form.

(b) Find the magnitude of the velocity of the aircraft relative to the air.

ANS:-40I+80j m/s