Physics-
General
Easy

Question

A cannon of a level plane is aimed at an angle theta above the horizontal and a shell is fired muzzle velocity v subscript 0 end subscript towards a cliff D distance away. The height at which the canon strikes the cliff is given by

  1. D sin invisible function application theta minus fraction numerator 1 over denominator 2 end fraction fraction numerator g D to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript sin to the power of 2 end exponent invisible function application theta end fraction  
  2. D cos invisible function application theta minus fraction numerator 1 over denominator 2 end fraction fraction numerator g D to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript sin to the power of 2 end exponent invisible function application theta end fraction  
  3. D tan invisible function application theta minus fraction numerator 1 over denominator 2 end fraction fraction numerator g D to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript cos to the power of 2 end exponent invisible function application theta end fraction  
  4. D tan invisible function application theta minus fraction numerator 1 over denominator 2 end fraction fraction numerator g D to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript sin to the power of 2 end exponent invisible function application theta end fraction  

The correct answer is: D tan invisible function application theta minus fraction numerator 1 over denominator 2 end fraction fraction numerator g D to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript cos to the power of 2 end exponent invisible function application theta end fraction


    Time taken to cover horizontal distance D with constant horizontal velocity, t equals D divided by v subscript 0 end subscript cos invisible function application theta. Taking vertical motion for time t, we have
    h equals v subscript 0 end subscript sin invisible function application theta cross times t minus fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
    equals v subscript 0 end subscript sin invisible function application theta cross times fraction numerator D over denominator v subscript 0 end subscript cos invisible function application theta end fraction minus fraction numerator 1 over denominator 2 end fraction g open parentheses fraction numerator D over denominator v subscript 0 end subscript cos invisible function application theta end fraction close parentheses to the power of 2 end exponent
    equals D tan invisible function application theta minus fraction numerator 1 over denominator 2 end fraction fraction numerator g D to the power of 2 end exponent over denominator v subscript 0 end subscript superscript 2 end superscript cos to the power of 2 end exponent invisible function application theta end fraction

    Related Questions to study

    General
    Physics-

    Two bodies are projected with the same velocity. If one is projected at an angle of 30 degree and the other at an angle of 60 degree to the horizontal, the ratio of the maximum heights reached is

    Two bodies are projected with the same velocity. If one is projected at an angle of 30 degree and the other at an angle of 60 degree to the horizontal, the ratio of the maximum heights reached is

    Physics-General
    General
    Physics-

    Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point C is

    Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point C is
    Physics-General

    General
    Physics-

    There are two forces each of magnitude 10 units. One inclined at an angle of 30degree and the other at an angle of 135degree to the positive direction of x minusaxis. The x and y components of the resultant are respectively.

    There are two forces each of magnitude 10 units. One inclined at an angle of 30degree and the other at an angle of 135degree to the positive direction of x minusaxis. The x and y components of the resultant are respectively.

    Physics-General
    parallel
    General
    Physics-

    If stack A with rightwards arrow on top=2 stack i with hat on top plus 3 stack j with hat on top plus 4 stack k with hat on top and stack B with rightwards arrow on top equals 4 stack i with hat on top plus 3 stack j with hat on top plus 2 stack k with hat on top, then angle between stack A with rightwards arrow on top and stack B with rightwards arrow on top is

    If stack A with rightwards arrow on top=2 stack i with hat on top plus 3 stack j with hat on top plus 4 stack k with hat on top and stack B with rightwards arrow on top equals 4 stack i with hat on top plus 3 stack j with hat on top plus 2 stack k with hat on top, then angle between stack A with rightwards arrow on top and stack B with rightwards arrow on top is

    Physics-General
    General
    Physics-

    A body is projected with initial velocity of left parenthesis 8 stack i with hat on top plus 6 stack j with hat on top right parenthesis m s to the power of negative 1 end exponent. The horizontal range is

    A body is projected with initial velocity of left parenthesis 8 stack i with hat on top plus 6 stack j with hat on top right parenthesis m s to the power of negative 1 end exponent. The horizontal range is

    Physics-General
    General
    Physics-

    A wheel completes 2000 revolutions to cover the 9.5 km distance, then the diameter of the wheel is

    A wheel completes 2000 revolutions to cover the 9.5 km distance, then the diameter of the wheel is

    Physics-General
    parallel
    General
    Physics-

    When a ceiling fan is switched on, it makes 10 rotations in the first 4 s. How many rotations will it make in the next 4 s? (Assuming uniform angular acceleration)

    When a ceiling fan is switched on, it makes 10 rotations in the first 4 s. How many rotations will it make in the next 4 s? (Assuming uniform angular acceleration)

    Physics-General
    General
    Physics-

    A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap is

    A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap is

    Physics-General
    General
    Physics-

    (stack P with rightwards arrow on top plus stack Q with rightwards arrow on top) is a unit vector along X-axis. If stack P with rightwards arrow on top equals stack i with hat on top minus stack j with hat on top plus stack k with hat on top comma then what value is stack Q with rightwards arrow on top ?

    (stack P with rightwards arrow on top plus stack Q with rightwards arrow on top) is a unit vector along X-axis. If stack P with rightwards arrow on top equals stack i with hat on top minus stack j with hat on top plus stack k with hat on top comma then what value is stack Q with rightwards arrow on top ?

    Physics-General
    parallel
    General
    Physics-

    A projectile is fired at an angle of 45 degree with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is:

    A projectile is fired at an angle of 45 degree with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is:

    Physics-General
    General
    Physics-

    A ball is projected with kinetic energy E at an angle of 45 degree to the horizontal. At the highest point during its flight, its kinetic energy will be

    A ball is projected with kinetic energy E at an angle of 45 degree to the horizontal. At the highest point during its flight, its kinetic energy will be

    Physics-General
    General
    Physics-

    In uniform circular motion, the velocity vector and acceleration vector are

    In uniform circular motion, the velocity vector and acceleration vector are

    Physics-General
    parallel
    General
    Physics-

    Two stones are projected from the same speed but making different angels with the horizontal. Their horizontal ranges are equal. The angle of projection of one is pi divided by 3 and the maximum height reached by it is 102 m. Then maximum height reached by the other in metre is

    Two stones are projected from the same speed but making different angels with the horizontal. Their horizontal ranges are equal. The angle of projection of one is pi divided by 3 and the maximum height reached by it is 102 m. Then maximum height reached by the other in metre is

    Physics-General
    General
    Physics-

    The range of particle when launched at an angle 15 degree with the horizontal is 1.5 km. What is the range of projectile when launched at an angle of 45 degree to the horizontal?

    The range of particle when launched at an angle 15 degree with the horizontal is 1.5 km. What is the range of projectile when launched at an angle of 45 degree to the horizontal?

    Physics-General
    General
    Physics-

    Neglecting the air resistance, the time of flight of a projectile is determined by

    Neglecting the air resistance, the time of flight of a projectile is determined by

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.