JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Kinematics

An object is projected in the air with initial velocity

u

at an angle

θ

. The projectile motion is such that the horizontal range R , is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ____ degree.

Answer: 15

Solution

Maximum range occurs at

θ = 4 5^{\circ}

R_{m a x} = \frac{u ^{2}}{g}

. For half the range:

\frac{R}{2} = \frac{u ^{2}}{2 g} = \frac{u ^{2} s i n 2 θ}{g}

. This gives

sin 2 θ = \frac{1}{2}

, so

2 θ = 3 0^{\circ}

15 0^{\circ}

, yielding

θ = 1 5^{\circ}

7 5^{\circ}

. The answer is 15 (the smaller angle).

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Integer answer

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 →