Question 264: Laws of Motion

Question

A projectile is thrown from a point O on the ground at an angle 45$$^\circ$$ from the vertical and with a speed 5$$\sqrt 2 $$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g = 10 m/s
2
.
The value of t is _____________.

Accepted Answer

Range, $$R = {u_x} 	imes T = {{2{u_x}{u_y}} \over g} = {{2 	imes 5 	imes 5} \over {10}} = 5$$ m
Time of flight, $$T = {{2{u_y}} \over g} = {{2 	imes 5} \over {10}} = 1$$ s
Both particle have no vertical velocity after splitting so both will take same time to reach the ground.
$$\because$$ Time of motion of one part falling vertically downwards is 0.5 s
$$\Rightarrow$$ Time of motion of another part, $$t = 0.5$$ s

Laws of Motion

Integer / Numeric Answer Type