Question:
Two bodies are projected from ground with same speeds $40\, ms ^{-1}$ at two different angles with respect to horizontal The bodies were found to have same range If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is ____$m$ (Given $g=10 ms ^{-2}$ )
Two bodies are projected from ground with same speeds $40\, ms ^{-1}$ at two different angles with respect to horizontal The bodies were found to have same range If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is ____$m$ (Given $g=10 ms ^{-2}$ )
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The maximum height attained by a projectile depends on its initial speed and the sine of the angle of projection.
Updated On: Mar 31, 2026
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Correct Answer: 80
Approach Solution - 1
The correct answer is 80.
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For projectile motion, the maximum height attained by a projectile is given by:
\[
H = \frac{v^2 \sin^2 \theta}{2g}
\]
The maximum height for the two projectiles, which are projected at angles \( 60^\circ \) and \( 30^\circ \), is:
\[
H_1 = \frac{40^2 \sin^2 60^\circ}{2 \times 10} = \frac{1600 \times \left( \frac{\sqrt{3}}{2} \right)^2}{20} = 40 \, \text{m}
\]
\[
H_2 = \frac{40^2 \sin^2 30^\circ}{2 \times 10} = \frac{1600 \times \left( \frac{1}{2} \right)^2}{20} = 20 \, \text{m}
\]
The sum of the maximum heights is:
\[
H_{\text{total}} = H_1 + H_2 = 40 + 20 = 80 \, \text{m}
\]
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration