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What is the term used for the angle at which an aerial photograph is taken?

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Important Questions on Trigonometric Functions

HARD
A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce (in meters) is _____________.
EASY
Two bodies are projected at angles θ and 90o-θ to the horizontal with the same speed. The ratio of their times of flight is
MEDIUM
A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is 
MEDIUM
Consider a triangular plot ABC with sides AB=7 m, BC=5 m and CA=6 m. A vertical lamp-post at the mid-point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is:
HARD
A mobile phone of mass 100 g falls from the hand of a person through the window of a train. The train is accelerating at 1 m s-2 and just 20 s have passed since it left the station from standstill. If the window is 2 m above the ground. With what kinetic energy will the phone will hit the ground? g=10 m s-2
EASY

The velocity of a projectile at the initial point A is 2i^-3j^ m s-1. Its velocity (in m s-1) at point B is

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HARD
If the angle of elevation of a cloud from a point P which is 25m above a lake be 30° and the angle of depression of reflection of the could in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is :
EASY
A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm s-1. How much work is needed to stop it?
HARD
A particle of mass 20 g is released with an initial velocity 5 m s-1 along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be: (Take g=10 m s-2)

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HARD

Two particles are simultaneously projected in the horizontal direction from a point P at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point P) are mutually perpendicular, is:

MEDIUM
Two balls are projected at an angle θ and (90°-θ) with respect to the horizontal with the same speed. The ratio of their maximum vertical heights is
EASY
Assertion: A stone of mass m kg is dropped vertically down from the window of a train which is at rest and then the same stone is dropped from the window of the train accelerating with a m s-1 . The net force in air acting on the stone is mg downward in both cases.

Reason: Vertical and horizontal motions are independent of each other in two dimensional projectile motion.
MEDIUM
A ball rolls off the edge of a horizontal table top 4 m high. If it strikes the floor at a point 5 m horizontally away from the edge of the table, what was its speed at the instant it left the table.
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A projectile can have the same range R for two angles of projection. If  t1 & t2 be the time of flights in the two cases, then the product of the two time of flights is proportional to
MEDIUM
A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to the fixed, and neglect air resistance.
EASY
The position vector of a particle R as a function of time is given by:

R=4sin2πti^+4cos2πtj^

Where R is in meters, t is in seconds and i^ and j^ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
MEDIUM
A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s-1 to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g=10 m s-2).
EASY
A projectile is thrown in the upward direction making an angle of 60o with the horizontal direction with a velocity of 147 m s-1. Then the time after which its inclination with the horizontal is 45o, is:
MEDIUM

Lionel Messi is practising chip shots in his trailer. His aim is to kick the ball in such a way that it hits the target. He must kick the ball with a speed of 40m/s w.r.t. the trailer at all times.


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Case 1:- His trailer moves with a constant velocity
Case 2:- The trailer rides off a cliff

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The angle with the horizontal (from the frame of the trailer) at which Messi should kick the ball in Case 2 is

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Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by

θt=tan-1(v0y-gtv0x)

where the symbols have their usual meaning.