Question

ms
5. A ball is thrown vertically upward and it reaches a height of 80 m. Find the velocity
with which it was thrown and time taken for reaching the ground after being
thrown. Take g = 10 ms?
​

Answer 1

Given :

$\sf{Distance\:travelled\:by\:the\:ball\:vertically \:=\:80m}$

$\sf{Acceleration\:due\:to\:gravity\:=\:10\:m/s}$

To find :

$\textsf{(i) Initial Velocity of the ball thrown }$

$\textsf{(ii) Time taken by the ball to reach the ground}$

Taken :

So , initial velocity (v) = 0

Final velocity (u) = 0

Distance travelled (h) = 80 m

Acceleration due to gravity (g) = -10 m/s

Time (t) = 0

And now we have got the value of all now , use this formula to find the velocity of the ball .

$\sf{\boxed{s=\dfrac{{v}^{2}}{2g}}}$

After find the velocity we have to find the time taken by the ball to come at ground .

Use , this formula to find the time taken ball to reach at ground .

$\sf{\boxed{v={u}^{2}-gt}}$

Solution :

|| 1 || Initial velocity :

$\sf{\implies{80\:m=\dfrac{{v}^{2}}{2\times\:10\:m/s}}}$

$\sf{\implies{80\:m=\dfrac{{v}^{2}}{20}}}$

$\sf{\implies{{v}^{2}=80\:m\times\:20}}$

$\sf{\implies{v=\sqrt{80\:m\times\:20}}}$

$\sf{\implies{v=\sqrt{1600}}}$

$\sf{\implies{v=40\:m/s}}$

________________________________

|| 2 || Time taken :

$\sf{\implies{40\:m/s=(0\times\:0)-10\:m/s\times\:t}}$

$\sf{\implies{40\:m/s=-10t}}$

$\sf{\implies{\dfrac{40\:m/s}{10}=t}}$

$\sf{\implies{4\:seconds =t}}$

Answer :

|| 1 ||

So , Initial velocity or velocity of the ball thrown is 40 m/s-¹ .

|| 2 ||

And the time taken by the ball to come back at ground is 4 seconds .