Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2011Paper 2
Exam
JEE Advanced
Year
2011
Paper
Paper 2
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Advanced 2011 · Paper 2 · Physics · Motion in Two Dimensions

A train is moving along a straight line with a constant...

A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a ball forward with a speed of 10 m/s10 \mathrm{~m} / \mathrm{s}, at an angle of 60∘60^{\circ} to the horizontal. The boy has to move forward by 1.15 m1.15 \mathrm{~m} inside the train to catch the ball back at the initial height. The acceleration of the train in m/s2\mathrm{m} / \mathrm{s}^2, is

Correct answer

5

Step-by-step solution

t=T=2usin⁡θg=2×10×sin⁡60∘10=3s\begin{aligned} t & =T=\frac{2 u \sin \theta}{g} \\ & =\frac{2 \times 10 \times \sin 60^{{}^{\circ}}}{10}=\sqrt{3} \mathrm{ s}\end{aligned}DisplacementoftrainintimeDisplacement of train in timet=\frac{1}{2} a t^2Displacementofboywithrespecttotrain=1.15Displacement of boy with respect to train =1.15\mathrm{ m}\thereforeDisplacementofboywithrespecttoground=Displacement of boy with respect to ground =\left(1.15+\frac{1}{2}a t²\right) Displacement of ball with respect to ground =(ucos⁡60∘)t=\left(u \cos 60^{{}^{\circ}}\right) t To catch the ball back at initial height, 1.15+12at2=(ucos⁡60∘)t∴1.15+\ffrac12a(3)2=10×12×3\begin{aligned} 1.15+\frac{1}{2}a t² & =\left(u \cos 60^{{}^{\circ}}\right) t \\ \therefore 1.15+\ffrac{1}{2}a(\sqrt{3})^2& =10 \times \frac{1}{2} \times \sqrt{3} \end{aligned}Solvingthisequation,wegeta=5ms−2Solving this equation, we get a=5 \mathrm{ ms}^{-2}\therefore Answer is 5. Analysis of Question (i) Question is moderately tough. (ii) Velocity of ball given in the question is with respect to ground.
Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle is thrown with a speed v from a point O at an angle θ with the horizontal… JEE Advanced 2026A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is… JEE Main 2026Two identical bodies, projected with the same speed at two different angles cover the… JEE Main 2026If x and y coordinates of a projectile as a function of time (t) are given as 24t and… JEE Main 2026A gun mounted on the ground fires bullets in all directions with same speed. The farthest… JEE Main 2026Two projectiles are projected with the same initial velocities at the 15^∘ and 30^∘ with… JEE Main 2026A boy throws a ball into air at 45^ ∘ from the horizontal to land it on a roof of a… JEE Main 2026An object is projected with kinetic energy K from a point A at an angle 60^ ∘ with the… JEE Main 2026 Full Motion in Two Dimensions list All JEE Advanced PYQs