Question:
Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?
Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?
Updated On: Apr 28, 2025
- $R^2 \, = \, 2 h_1 h_2$
- $R^2 \, = \, 16 h_1 h_2$
- $R^2 \, = \, 4 h_1 h_2$
- $R^2 \, = \, h_1 h_2$
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The Correct Option is B
Solution and Explanation
For same range angle of projection will be $\theta$ &
$90 - \theta$
$R = \frac{u^2 2 sin \theta cos \theta}{g}$
$h_1 = \frac{u^2 sin^2 \theta}{g}$
$h_2 = \frac{u^2 sin^2 (90 - \theta}{g}$
$\frac{R^2}{h_1h_2} = 16$
$90 - \theta$
$R = \frac{u^2 2 sin \theta cos \theta}{g}$
$h_1 = \frac{u^2 sin^2 \theta}{g}$
$h_2 = \frac{u^2 sin^2 (90 - \theta}{g}$
$\frac{R^2}{h_1h_2} = 16$
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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