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/s ^{2}, has v_{o} = ( 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:
56.4 ^{o} 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 ,
14 ^{o} east of north.
**

**Q5.
A football is kicked off with an initial speed of 19.5 m/s at an angle of
45 ^{o} 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 60 ^{o} 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/s ^{2}.
At some instant, the magnitude of the total acceleration is 3 m/s^{2 }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
3.85x10 ^{8} 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/s ^{2}.
**

**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 51 ^{o}
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
**

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