Question

An object thrown vertically upwards reaches a height of $500m$. What was its initial velocity? How long will the object take to come back to the earth? Assume $g=10m{s}^{-2}$.

• A. $50m{s}^{-1}$ and $5s$
• B. $100m{s}^{-1}$ and $20s$
• C. $200m{s}^{-1}$ and $40s$
• D. $300m{s}^{-1}$ and $30s$

Answer 1

The correct option is B $100m{s}^{-1}$ and $20s$

Assume upward direction to be positive.
Given:
Maximum height is: $H=500m$
Acceleration due to gravity, $g=-10m{s}^{-2}$

Consider the motion from the initial point to the highest point.
Displacement: $s=+H=500m$
Final velocity is zero because the object is at rest at the highest point.
$v=0$

Using equation of motion:
$v^2=u^2+2as$
$0^2=u^2+2\times (-10)\times 500$
$u=\pm 100m/s$

Initial velocity is in the upward direction. So, $u=+100m/s$

Consider the motion from the initial point to the final point.
Let the total time taken to come back to the earth be $t$
Initital position and the final position is the same. So, the displacement is zero.
$s=0$
Initial velocity, $v=100m/s$
Using equation of motion,
$s=ut+\frac{1}{2}g{t}^2$
$0=100\times t+\frac{1}{2}\times (-10)\times t^2$
$t=20s$ or $t=0s$

Time to return is greater than $0s$. So, $t=20s$