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PROJECTILES
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Q1) Find time taken by the
projectile to reach the ground when thrown at an angle of 
with x axis (in
upward direction) from the top of tower
of height “h” . [Sol : 
]
with x axis (in
upward direction) from the top of tower
of height “h” . [Sol : ]
Q2) Find time taken by the
projectile to reach the ground when thrown at an angle of with x axis (in
downward direction) from the top of tower of height “h” . [Sol
: 
]
with x axis (in
downward direction) from the top of tower of height “h” . [Sol
: ]
Q3) Find Range, max range and time of flight of a
projectile when it is thrown up at an inclined plane at an angle of with ground and given
that angle of inclined plane is 
.[Sol : 
,
with ground and given
that angle of inclined plane is .[Sol : ,
, 
]
Q4) Find Range and time of flight of a projectile when
it is thrown down at an inclined plane at an angle of with x axis and given
that angle of inclined plane is . [Sol:
, 
]
with x axis and given
that angle of inclined plane is . [Sol:, ]
Q5) Two bodies are projected from
the same point with equal speeds in such a
direction that they both strikes the same point on a plane whose
inclination is 
. If is angle of projection
of first body with horizontal then find the ratio of their time of
flights. [Sol : 
]
. If is angle of projection
of first body with horizontal then find the ratio of their time of
flights. [Sol : ]
Q6)
Show that there are two values of time for which a projectile is at the same
height Also show mathematically that the sum of these two times is equal to the
time of flight.
Q7)
A particle A is projected with an initial velocity of 60m/s at an angle 
to the horizontal. At the same time a second particle
B is projected in opposite direction with initial speed of 50 m/s from a point
at a distance of 100 m from A. If the particles collide in air, find (a) the
angle of projection of particle B,
(b) time when the collision takes place and (c) the distance of P from A, where
collision occurs. 
[Sol : 
]
to the horizontal. At the same time a second particle
B is projected in opposite direction with initial speed of 50 m/s from a point
at a distance of 100 m from A. If the particles collide in air, find (a) the
angle of projection of particle B,
(b) time when the collision takes place and (c) the distance of P from A, where
collision occurs. [Sol : ]
Q8)
A car accelerating at the rate of 
from rest from
origin is carrying a man at the rear end who has a gun in his hand. The car is
always moving along positive x-axis. At
t = 4 s, the man fires from the gun and the bullet hits a bird at t =
8s. The bird has a position vector 
Find velocity of projection of the bullet. Take the
y-axis in the horizontal plane. 
)
from rest from
origin is carrying a man at the rear end who has a gun in his hand. The car is
always moving along positive x-axis. At
t = 4 s, the man fires from the gun and the bullet hits a bird at t =
8s. The bird has a position vector Find velocity of projection of the bullet. Take the
y-axis in the horizontal plane. )
[Sol : 
]
]
Q9) The velocity of a projectile when it is at
the greatest height is 
times its velocity when it is at half of its greatest
height. Determine its angle of projection.
[Sol : 600]
times its velocity when it is at half of its greatest
height. Determine its angle of projection.
[Sol : 600]
Q10) A particle is thrown over a triangle from one
end of a horizontal base and after grazing the vertex falls on the other end of
the base. If and be the base angles and the angle of p0rojection, prove that 
and be the base angles and the angle of p0rojection, prove that
Q11)
A ball is projected horizontally in air such that it moves with a constant
horizontal acceleration a due to air flow. Taking the gravitational
acceleration into account. Find the (a) velocity (b) acceleration as the
function of time till it strikes the ground.
[Sol : 
]
]
Q12)
A particle is projected with a velocity 
onto a horizontal plane, find the:
onto a horizontal plane, find the:
(a) Time of flight [Sol
: 0.8 secs]
(b) maximum height [Sol : 0.8 m]
(c) Horizontal range [Sol : 2.4 m]
(d) Velocity at 
[Sol : 
]
[Sol : ]
(e) Equation of trajectory [Sol : 
]
] 
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