Home
Class 11
PHYSICS
The range of a projectile at an angle th...

The range of a projectile at an angle `theta` is equal to half of the maximum range if thrown at the same speed. The angel of projection `theta` is given by

Text Solution

Verified by Experts

We know: `R = (u^2 sin 2 theta)/(g) and R_(max) = (u^2)/(g)`.
Given `R = (1)/(2) R_(max)`
or `R = (u^2 sin 2 theta)/(g) = (1)/(2) R_(max) = (u^2)/(2 g)`
`rArr sin 2 theta = (1)/(2) or 2 theta = 30^@ rArr theta = 15^@`
Also `R = (u^2 sin (pi - 2 theta))/(g)`
Now, `sin(pi - 2 theta) = (1)/(2) rArr 180^@ - 2 theta = 30^@ rArr theta = 75^@`.
Promotional Banner

Topper's Solved these Questions

  • KINEMATICS-2

    CENGAGE PHYSICS|Exercise Solved Examples|7 Videos

  • KINEMATICS-2

    CENGAGE PHYSICS|Exercise Exercise 5.1|15 Videos

  • KINEMATICS-1

    CENGAGE PHYSICS|Exercise Integer|9 Videos

  • KINETIC THEORY OF GASES

    CENGAGE PHYSICS|Exercise Compression|2 Videos

Similar Questions

Explore conceptually related problems

The horizontal range is equal to two times maximum height of a projectile. The angle of projection ofthe projectile is:

The range of a projectile when launched at angle theta is same as when launched at angle 2theta . What is the value of theta ?

Two balls are thrown with the same speed from a point O at the same time so that their horizontal ranges are same. If the difference of the maximum height attained by them is equal to half of the sum of the maximum heights, then the angles of projection for the balls are

The range of a projectile fired at an angle of 15^@ is 50 m. If it is fired with the same speed at an angle of 45^@ its range will be

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

The question given below consist of an assertion and the reason . Use the following key to choose appropriate answer: Assertion: Range of projectile motion is same when particle is projected at an angle theta with the horizontal or at an angle (90^(@) -theta) with the horizontal . Reason : Range of projectile motion depended only on the angle of projection.

A projectile is thrown with velocity v at an angle theta with the horizontal. When the projectile is at a height equal to half of the maximum height,. The vertical component of the velocity of projectile is.

A projectile is thrown with velocity v at an angle theta with the horizontal. When the projectile is at a height equal to half of the maximum height,. The velocity of the projectile when it is at a height equal to half of the maximum height is.

Range of a projectile is R, when the angle of projection is 30^(@) . Then, the value of the other angle of projection for the same range is