Two stones are thrown up simultaneously with | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the positions of the two stones be $x_1(t)$ and $x_2(t)$.For $0 \le t \le 6 \, s$,both stones are in the air under gravity $g$. Their position

Vedclass · Accepted Answer

Vedclass · Answer

(A) Let the positions of the two stones be $x_1(t)$ and $x_2(t)$.For $0 \le t \le 6 \, s$,both stones are in the air under gravity $g$. Their positions are $x_1(t) = u_1 t - \frac{1}{2} g t^2$ and $x_2(t) = u_2 t - \frac{1}{2} g t^2$.The relative position is $\Delta x = x_2 - x_1 = (u_2 - u_1) t$. Since $u_2 > u_1$,this is a linear function of $t$ starting from $0$ at $t = 0$ and increasing until $t = 6 \, s$.At $t = 6 \, s$,the first stone hits the ground,so $x_1(6) = 0$. For $6 \, s The relative position is $\Delta x = x_2 - 0 = u_2 t - \frac{1}{2} g t^2$. This is a downward-opening parabola.At $t = 10 \, s$,the second stone hits the ground,so $x_2(10) = 0$,making $\Delta x = 0$.Thus,the graph is a straight line from $t = 0$ to $t = 6 \, s$ and a parabolic curve from $t = 6 \, s$ to $t = 10 \, s$. This matches the first graph.

Similar Questions

$A$ ball is dropped from a building of height $45 \, m$. Simultaneously,another ball is thrown up with a speed of $40 \, ms^{-1}$. Calculate the relative speed of the balls as a function of time.

$A$ car is standing $200\, m$ behind a bus,which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has an acceleration of $2\, m/s^2$ and the car has an acceleration of $4\, m/s^2$. The car will catch up with the bus after a time of:

Two particles $A$ and $B$ are moving along a straight line with $B$ ahead of $A$. If their velocities remain constant,what will be the effect on the magnitude of their relative velocity when $A$ is ahead of $B$?

An express train is moving with a velocity $v_1$. Its driver finds another train moving on the same track in the same direction with velocity $v_2$. To escape a collision,the driver applies a retardation $a$ to the train. The minimum time to escape a collision will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module