Question

a particle is thrown horizontally with speed of 10 m/s at t = 0 from a tower of height 100 m. then the speed of particle at t = 2 second is

Answer 1

consider the horizontal direction along x-axis and vertical direction along y-axis with down as positive direction of motion

$\underset{v_{o}}{\rightarrow}$ = initial velocity of the particle = 10 $\hat{i}$ + 0 $\hat{j}$

$\underset{a}{\rightarrow}$ = acceleration of the particle = 0 $\hat{i}$ - 9.8 $\hat{j}$

t = time of travel = 2 sec

$\underset{v_{f}}{\rightarrow}$ = final velocity of the particle

final velocity of the particle using the kinematics equation is given as

$\underset{v_{f}}{\rightarrow}$ = $\underset{v_{o}}{\rightarrow}$ + ($\underset{a}{\rightarrow}$ ) t

$\underset{v_{f}}{\rightarrow}$ = (10 $\hat{i}$ + 0 $\hat{j}$) + (0 $\hat{i}$ - 9.8 $\hat{j}$) (2)

$\underset{v_{f}}{\rightarrow}$ = 10 $\hat{i}$ - 19.6 $\hat{j}$

speed using Pythagorean theorem is given as

v = sqrt((10)² + (- 19.6)²)

v = 22 m/s