Two objects are projected with same velocity 'u' however at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha+\beta=90^{\circ}$, the ratio of horizontal range of the first object to the $2^{\text {nd}}$ object will be :

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Kinematics

Two objects are projected with same velocity 'u' however at different angles

α

and

β

with the horizontal. If

α + β = 9 0^{\circ}

, the ratio of horizontal range of the first object to the

2^{nd}

object will be :

(A) $4 : 1$
(B) $2 : 1$
(C) $1 : 2$
(D) $1 : 1$ ✓ Correct

Answer: (D)

Solution

The range depends on the launch angle through

R = \frac{u ^{2} sin 2 θ}{g}

. For the second angle

β = 9 0^{\circ} - α

sin 2 β = sin (18 0^{\circ} - 2 α) = sin 2 α

, the very factor that sets the first range. Launched with equal speeds, the two bodies cover equal horizontal distances, a ratio of

1 : 1

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Kinematics →

More JEE Main questions on Kinematics

A projectile is thrown upward at an angle $6 0^{\circ}$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $4 5^{\circ}$ with the horizontal. The initial speed of the projectile is ______ m/s.
JEE Main 2026View solution →
A river of width 200 m is flowing from west to east with a speed of $18 km / h$ . A boat, moving with speed of $36 km / h$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for thi …
JEE Main 2026View solution →
An object is projected with kinetic energy K from a point A at an angle $6 0^{\circ}$ with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :
JEE Main 2026View solution →
A block is sliding down on an inclined plane of slope $θ$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$ . The distance $(S)$ travelled by the block before its velocity become zero, …
JEE Main 2026View solution →
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 m / s^{2}$ . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is …
JEE Main 2026View solution →
A bead $P$ sliding on a frictionless semi-circular string $(A C B)$ and it is at point $S$ at $t = 0$ and at this instant the horizontal component of its velocity is $v$ . Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t = 0$ …
JEE Main 2026View solution →