1
JEE Main 2024 (Online) 27th January Evening Shift
Numerical
+4
-1

A body falling under gravity covers two points $$A$$ and $$B$$ separated by $$80 \mathrm{~m}$$ in $$2 \mathrm{~s}$$. The distance of upper point A from the starting point is _________ $$\mathrm{m}$$ (use $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$).

2
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1

A particle starts from origin at $$t=0$$ with a velocity $$5 \hat{i} \mathrm{~m} / \mathrm{s}$$ and moves in $$x-y$$ plane under action of a force which produces a constant acceleration of $$(3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2$$. If the $$x$$-coordinate of the particle at that instant is $$84 \mathrm{~m}$$, then the speed of the particle at this time is $$\sqrt{\alpha} \mathrm{~m} / \mathrm{s}$$. The value of $$\alpha$$ is _________.

3
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1

A projectile fired at $$30^{\circ}$$ to the ground is observed to be at same height at time $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ after projection, during its flight. The speed of projection of the projectile is ___________ $$\mathrm{m} ~\mathrm{s}^{-1}$$.

(Given $$g=10 \mathrm{~ms}^{-2}$$ )

4
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

For a train engine moving with speed of $$20 \mathrm{~ms}^{-1}$$, the driver must apply brakes at a distance of 500 $$\mathrm{m}$$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $$\sqrt{x} \mathrm{~ms}^{-1}$$. The value of $$x$$ is ____________.

(Assuming same retardation is produced by brakes)