Question

A rock is thrown straight up and reaches a height of 10 m. a) How long was the rock in the air? b) What is the initial velocity of the rock?

Answer 1

Given :

Maximum height attained = 10m

To Find :

• Time taken by rock to reach there
• Initial velocity of the rock

Solution :

❒ For a body thrown vertically upward, g is taken negative.

• Acceleration due to gravity has constant magnitude throughout the motion therefore equation of motion can be easily applied to solve this question.

A] Calculation of Initial velocity :

$\sf:\implies\:v^2-u^2=2gH$

• At highest point v = 0

$\sf:\implies\:0^2-u^2=2(-10)(10)$

$\sf:\implies\:-u^2=-200$

$\sf:\implies\:u=\sqrt{200}$

$:\implies\:\underline{\boxed{\bf{\red{u=10\sqrt2\:m/s}}}}$

B] Calculation of time :

$\sf:\implies\:v=u+gt$

$\sf:\implies\:0=10\sqrt2+(-10)t$

$\sf:\implies\:-10\sqrt2=-10t$

$:\implies\:\underline{\boxed{\bf{\pink{t=\sqrt2\:s}}}}$