JEE Main · 2007 · 29 Apr 2007 · Offline · Kinematics

A particle is projected at

6 0^{\circ}

to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

(A)K
(B)Zero
(C) $K /2$
(D) $K /4$ ✓ Correct

Answer: (D)

Solution

At launch the kinetic energy is

K = \frac{1}{2} m v^{2}

. At the top of the trajectory only the horizontal part of the velocity survives,

v_{x} = v cos 6 0^{\circ} = \frac{v}{2}

, while the vertical component is momentarily zero. The kinetic energy there is

\frac{1}{2} m v_{x}^{2} = \frac{1}{2} m (\frac{v}{2})^{2} = \frac{K}{4}

JEE Main · 2007 · 29 Apr 2007 · Offline · 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 →