Home
Class 11
PHYSICS
A particle is thrown over a triangle fro...

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 `alpha and beta` be the base angles and `theta` the angle of projection, prove that `tan theta = tan alpha + tan beta` .

Text Solution

Verified by Experts

The correct Answer is:
A
The situation is shown in figure.

From figure, we have
`tan alpha + tan beta = y/x + y/(R-x)`
`tan alpha + tan beta = (yR)/(x(R-x))`……….(i)
Equation of trajectory is
`y = x tan theta [1-x/R]`
or, ` tan theta = (yR)/(x(R-x))` ........(ii)
From Eqs. (i) and (ii), we have
`tan theta = tan alpha + tan beta`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROJECTILE MOTION

    DC PANDEY ENGLISH|Exercise Exercise 7.1|5 Videos

  • PROJECTILE MOTION

    DC PANDEY ENGLISH|Exercise Exercise 7.2|10 Videos

  • PROJECTILE MOTION

    DC PANDEY ENGLISH|Exercise Example Type 5|3 Videos

  • MOTION IN A PLANE

    DC PANDEY ENGLISH|Exercise (C )Medical entrances gallery|32 Videos

  • PROPERTIES OF MATTER

    DC PANDEY ENGLISH|Exercise Integer|8 Videos

Similar Questions

Explore conceptually related problems

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 30^(@) and 60^(@) be the base angles and theta the angle of projection then tan theta is

If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta), prove that tan theta/2=+-tan alpha/2 cot beta/2.

If alpha and beta are roots of the equation a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

A shell fired from the base of a mountain just clears it. If alpha is the angle of projection, then the angular elevation of the summit beta is

If alpha and beta are acute such that alpha+beta and alpha-beta satisfy the equation tan^(2)theta-4tan theta+1=0 , then (alpha, beta ) =

alpha and beta are acute angles and cos2alpha = (3cos2beta-1)/(3-cos2beta) then tan alpha cot beta =

Two particles are projected at the same instant from the same point at inclinations alpha and beta to the horizontal. If they simultaneously hit the top and bottom of a vertical pole subtending angle theta at the point of projection , find (tan alpha - tan beta) .

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

Two parallel straight lines are inclined to the horizon at an angle prop . A particle is projected from a point mid way between them so as to graze one of the lines and strikes the other at right angle. Show that if theta is the angle between the direction of projection and either of lines, then tan theta = (sqrt(2 - 1)) cot prop .

A train travelling on one of two intersecting railway lines, subtends at a certain station on the other line, an/ angle alpha when the front of the carriage reaches the junction and an angle beta when the end of the carriage reaches it. Then, the two lines are inclined to each other at an angle theta , show that 2 cot theta=cot alpha-cot beta cot alpha + cot beta

Home
Profile